##
##
## Attaching package: 'RSDA'
## The following objects are masked from 'package:stats':
##
## cor, sd, var
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
## Linking to GEOS 3.7.2, GDAL 3.0.4, PROJ 6.3.2; sf_use_s2() is TRUE
##
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
##
## last_plot
## The following object is masked from 'package:stats':
##
## filter
## The following object is masked from 'package:graphics':
##
## layout
n=100
x1.lower <- round(runif(n,0,2),2)
x1.upper <- x1.lower + round(runif(n,1,2))
x2.lower <- round(runif(n,0,2),2)
x2.upper <- x2.lower + round(runif(n,1,2))
x3.lower <- round(runif(n,0,2),2)
x3.upper <- x3.lower + round(runif(n,1,2))
x1.centers <- (x1.lower+x1.upper)/2
x2.centers <- (x2.lower+x2.upper)/2
x3.centers <- (x3.lower+x3.upper)/2
x1.ranks <- (x1.upper-x1.lower)/2
x2.ranks <- (x2.upper-x2.lower)/2
x3.ranks <- (x3.upper-x3.lower)/2
y.centers <- 0.6*x1.centers + 0.3*x2.centers + 0.1*x3.centers
y.ranks <- 0.6*x1.ranks + 0.3*x2.ranks + 0.1*x3.ranks
y.lower <- y.centers - y.ranks
y.upper <- y.centers + y.ranks
tabla <- data.frame(x1.lower,x1.upper,x2.lower,x2.upper,x3.lower,x3.upper,y.lower,y.upper, x1.centers, x1.ranks,x2.centers,x2.ranks,x3.centers,x3.ranks, y.centers, y.ranks)
#Gráficamente
library(patchwork)
# Rectángulos (x1, y)
p1 <- ggplot(tabla, aes(xmin = x1.lower, xmax = x1.upper, ymin = y.lower, ymax = y.upper)) +
geom_rect(fill = "skyblue", color = "black", alpha = 0.4) +
geom_point(aes(x = x1.centers, y = y.centers), color = "red", size = 1) +
labs(title = "Rectángulos en el plano (x1, y)", x = "x1", y = "y") +
theme_minimal()
# (x2, y)
p2 <- ggplot(tabla, aes(xmin = x2.lower, xmax = x2.upper, ymin = y.lower, ymax = y.upper)) +
geom_rect(fill = "palegreen", color = "black", alpha = 0.4) +
geom_point(aes(x = x2.centers, y = y.centers), color = "red", size = 1) +
labs(title = "Rectángulos en el plano (x2, y)", x = "x2", y = "y") +
theme_minimal()
# (x3, y)
p3 <- ggplot(tabla, aes(xmin = x3.lower, xmax = x3.upper, ymin = y.lower, ymax = y.upper)) +
geom_rect(fill = "salmon", color = "black", alpha = 0.4) +
geom_point(aes(x = x3.centers, y = y.centers), color = "red", size = 1) +
labs(title = "Rectángulos en el plano (x3, y)", x = "x3", y = "y") +
theme_minimal()
p1## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Estimating R2 Geom for variable = 2
## Estimating R2 Geom for variable = 3
## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Estimating R2 Geom for variable = 2
## Estimating R2 Geom for variable = 3
## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Estimating R2 Geom for variable = 2
## Estimating R2 Geom for variable = 3
geom_indicesc <- indice1$results[[1]]$geom_indices
geom_indicescmenosr <- indice2$results[[1]]$geom_indices
geom_indicescmasr <- indice3$results[[1]]$geom_indices
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicesc$label <- "centros"
geom_indicescmenosr$label <- "centros menos rangos"
geom_indicescmasr$label <- "centros más rangos"
data_combined <- rbind(geom_indicesc,geom_indicescmenosr,geom_indicescmasr)
data_combined1 <- rbind(geom_indicescmenosr1, geom_indicescmasr1)
data_combined1 <- rbind(c(0,1),data_combined1)
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica con datos uniformes",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.
#Área acumulada entre las curvas: centros menos rangos y centros más rangos.
library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmenosr1$alpha, geom_indicescmasr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
table.diff <- cbind(alpha.vals, diff.geom_corr)
table.diff## alpha.vals diff.geom_corr
## [1,] 0.006403124 -6.118289e-06
## [2,] 0.011000000 2.696153e-05
## [3,] 0.026500000 1.066538e-04
## [4,] 0.027856777 1.564911e-04
## [5,] 0.028792360 1.858687e-04
## [6,] 0.030500000 2.594634e-04
## [7,] 0.030675723 3.246862e-04
## [8,] 0.030805844 4.292464e-04
## [9,] 0.031764760 6.722323e-04
## [10,] 0.032649655 9.877870e-04
## [11,] 0.035032128 1.095374e-03
## [12,] 0.036619667 1.159084e-03
## [13,] 0.037696154 1.311225e-03
## [14,] 0.038160844 1.412498e-03
## [15,] 0.040012498 1.756081e-03
## [16,] 0.040311289 1.782774e-03
## [17,] 0.040816663 1.829525e-03
## [18,] 0.042201896 2.065869e-03
## [19,] 0.042216703 2.617354e-03
## [20,] 0.042252219 2.848080e-03
## [21,] 0.042426407 3.087585e-03
## [22,] 0.042438190 3.395552e-03
## [23,] 0.042898135 3.649410e-03
## [24,] 0.043139309 3.853019e-03
## [25,] 0.043660623 4.298264e-03
## [26,] 0.044821870 4.840319e-03
## [27,] 0.045069391 5.260976e-03
## [28,] 0.046446205 6.087293e-03
## [29,] 0.046960089 6.574999e-03
## [30,] 0.047087684 7.373194e-03
## [31,] 0.047563116 7.762183e-03
## [32,] 0.047762433 7.908817e-03
## [33,] 0.048383882 8.360825e-03
## [34,] 0.050022495 9.365393e-03
## [35,] 0.050159745 1.041492e-02
## [36,] 0.050358713 1.115034e-02
## [37,] 0.050990195 1.197852e-02
## [38,] 0.051662365 1.307496e-02
## [39,] 0.052354560 1.390031e-02
## [40,] 0.052430907 1.397356e-02
## [41,] 0.052680642 1.388489e-02
## [42,] 0.052841745 1.402522e-02
## [43,] 0.053667961 1.419416e-02
## [44,] 0.053851648 1.495577e-02
## [45,] 0.054120237 1.520881e-02
## [46,] 0.054600824 1.538695e-02
## [47,] 0.054644304 1.481873e-02
## [48,] 0.055020451 1.475735e-02
## [49,] 0.055056789 1.487447e-02
## [50,] 0.055145263 1.515439e-02
## [51,] 0.055454937 1.516320e-02
## [52,] 0.055509008 1.517786e-02
## [53,] 0.055832338 1.515976e-02
## [54,] 0.055901699 1.630065e-02
## [55,] 0.056189412 1.773492e-02
## [56,] 0.056293872 1.778004e-02
## [57,] 0.056703175 1.877597e-02
## [58,] 0.056797887 1.900861e-02
## [59,] 0.057008771 1.992377e-02
## [60,] 0.057116110 2.040007e-02
## [61,] 0.057404268 2.157914e-02
## [62,] 0.057870545 2.280508e-02
## [63,] 0.057974132 2.289241e-02
## [64,] 0.058148517 2.266528e-02
## [65,] 0.059002119 2.317638e-02
## [66,] 0.059052942 2.322531e-02
## [67,] 0.059600755 2.441953e-02
## [68,] 0.060299254 2.458108e-02
## [69,] 0.060827625 2.476379e-02
## [70,] 0.060911822 2.575712e-02
## [71,] 0.061491869 2.630082e-02
## [72,] 0.061491869 2.630082e-02
## [73,] 0.062201286 2.666085e-02
## [74,] 0.062801274 2.677900e-02
## [75,] 0.063158531 2.649514e-02
## [76,] 0.063198101 2.680937e-02
## [77,] 0.063294945 2.702761e-02
## [78,] 0.063631753 2.763639e-02
## [79,] 0.063641574 2.763707e-02
## [80,] 0.063994140 2.803949e-02
## [81,] 0.064437955 2.914692e-02
## [82,] 0.064693508 2.934165e-02
## [83,] 0.064809336 2.943948e-02
## [84,] 0.065069194 2.950416e-02
## [85,] 0.065094163 2.956546e-02
## [86,] 0.065192024 3.098250e-02
## [87,] 0.066001894 3.140167e-02
## [88,] 0.066009469 3.140059e-02
## [89,] 0.066098411 3.138928e-02
## [90,] 0.066387122 3.161825e-02
## [91,] 0.066640828 3.225138e-02
## [92,] 0.066753277 3.321284e-02
## [93,] 0.067529623 3.378145e-02
## [94,] 0.067581432 3.470257e-02
## [95,] 0.067603624 3.473862e-02
## [96,] 0.068014704 3.539369e-02
## [97,] 0.068900290 3.624195e-02
## [98,] 0.069500000 3.652106e-02
## [99,] 0.070087445 3.678143e-02
## [100,] 0.070301138 3.816866e-02
## [101,] 0.072277244 3.856071e-02
## [102,] 0.072527581 3.862762e-02
## [103,] 0.072670489 3.968742e-02
## [104,] 0.073015409 4.051657e-02
## [105,] 0.073681748 4.167336e-02
## [106,] 0.074546965 4.184105e-02
## [107,] 0.074546965 4.184105e-02
## [108,] 0.075000000 4.154881e-02
## [109,] 0.075208045 4.131676e-02
## [110,] 0.075208045 4.479916e-02
## [111,] 0.075325958 4.475621e-02
## [112,] 0.075802375 4.583546e-02
## [113,] 0.076216796 4.631638e-02
## [114,] 0.076500000 4.665878e-02
## [115,] 0.076557168 4.627090e-02
## [116,] 0.076609399 4.632900e-02
## [117,] 0.077162167 4.701601e-02
## [118,] 0.077388630 4.817735e-02
## [119,] 0.077828337 5.002006e-02
## [120,] 0.078262379 5.251412e-02
## [121,] 0.078461774 5.251683e-02
## [122,] 0.078492038 5.192212e-02
## [123,] 0.078773409 5.107582e-02
## [124,] 0.079323704 5.123663e-02
## [125,] 0.079342612 5.007171e-02
## [126,] 0.079657078 5.006685e-02
## [127,] 0.080263628 5.087534e-02
## [128,] 0.080721744 5.230496e-02
## [129,] 0.081610355 5.408661e-02
## [130,] 0.081891697 5.668546e-02
## [131,] 0.082000000 5.783802e-02
## [132,] 0.082384768 6.186581e-02
## [133,] 0.082947272 6.230700e-02
## [134,] 0.083103851 6.231279e-02
## [135,] 0.083798866 6.187334e-02
## [136,] 0.083815273 6.186064e-02
## [137,] 0.084559151 6.120535e-02
## [138,] 0.084824819 6.109828e-02
## [139,] 0.085248167 6.130120e-02
## [140,] 0.085328776 6.033051e-02
## [141,] 0.085616879 6.027363e-02
## [142,] 0.085912746 6.184319e-02
## [143,] 0.086204698 6.198819e-02
## [144,] 0.086227896 6.072567e-02
## [145,] 0.086227896 6.072567e-02
## [146,] 0.086278618 6.037449e-02
## [147,] 0.086863399 6.160163e-02
## [148,] 0.086989942 6.069710e-02
## [149,] 0.087097646 6.090516e-02
## [150,] 0.087458562 6.121579e-02
## [151,] 0.088255311 6.153403e-02
## [152,] 0.089140339 6.236818e-02
## [153,] 0.089269256 6.254565e-02
## [154,] 0.090138782 6.488358e-02
## [155,] 0.090138782 6.488358e-02
## [156,] 0.091685604 6.770559e-02
## [157,] 0.093017471 6.971890e-02
## [158,] 0.093107465 6.687732e-02
## [159,] 0.093178592 6.698685e-02
## [160,] 0.093553461 6.841016e-02
## [161,] 0.095117033 6.872797e-02
## [162,] 0.095524866 6.808070e-02
## [163,] 0.096130120 6.772714e-02
## [164,] 0.097186676 6.798047e-02
## [165,] 0.097325485 7.048992e-02
## [166,] 0.097514102 7.512871e-02
## [167,] 0.098184775 7.825055e-02
## [168,] 0.098508883 8.072670e-02
## [169,] 0.099575348 8.452323e-02
## [170,] 0.100101199 8.504184e-02
## [171,] 0.100623059 8.470518e-02
## [172,] 0.100778222 8.396430e-02
## [173,] 0.101212647 8.441307e-02
## [174,] 0.102415819 8.519613e-02
## [175,] 0.103077641 8.547402e-02
## [176,] 0.103712343 8.499195e-02
## [177,] 0.104000000 8.439348e-02
## [178,] 0.105475116 8.431838e-02
## [179,] 0.105905618 8.524624e-02
## [180,] 0.105990566 8.547258e-02
## [181,] 0.107070071 8.763472e-02
## [182,] 0.107178589 9.090856e-02
## [183,] 0.108632408 9.795452e-02
## [184,] 0.108908218 1.025224e-01
## [185,] 0.110163515 1.052431e-01
## [186,] 0.110205490 1.045477e-01
## [187,] 0.110222502 1.030570e-01
## [188,] 0.110500000 9.958888e-02
## [189,] 0.110613064 9.978326e-02
## [190,] 0.111230616 1.015046e-01
## [191,] 0.111507847 1.052727e-01
## [192,] 0.112044634 1.079951e-01
## [193,] 0.112695386 1.113777e-01
## [194,] 0.112787411 1.118156e-01
## [195,] 0.113715654 1.128297e-01
## [196,] 0.114127122 1.134752e-01
## [197,] 0.114284732 1.135297e-01
## [198,] 0.114808536 1.149364e-01
## [199,] 0.115004348 1.158518e-01
## [200,] 0.115524889 1.171420e-01
## [201,] 0.115932092 1.162076e-01
## [202,] 0.116914499 1.187607e-01
## [203,] 0.117517020 1.205514e-01
## [204,] 0.118013770 1.206411e-01
## [205,] 0.118309974 1.175630e-01
## [206,] 0.118431415 1.160874e-01
## [207,] 0.119189974 1.155850e-01
## [208,] 0.120016666 1.169156e-01
## [209,] 0.120016666 1.169156e-01
## [210,] 0.120203993 1.183568e-01
## [211,] 0.120440857 1.222073e-01
## [212,] 0.120917327 1.245974e-01
## [213,] 0.120933866 1.246671e-01
## [214,] 0.121594613 1.270318e-01
## [215,] 0.121594613 1.270318e-01
## [216,] 0.121597697 1.253183e-01
## [217,] 0.122576507 1.253014e-01
## [218,] 0.122918672 1.244533e-01
## [219,] 0.123693169 1.241962e-01
## [220,] 0.123916302 1.241683e-01
## [221,] 0.124233651 1.292127e-01
## [222,] 0.125905719 1.298872e-01
## [223,] 0.126178445 1.287585e-01
## [224,] 0.126289350 1.272850e-01
## [225,] 0.126822711 1.272064e-01
## [226,] 0.127059041 1.268223e-01
## [227,] 0.127059041 1.255831e-01
## [228,] 0.127910125 1.242499e-01
## [229,] 0.128363741 1.240880e-01
## [230,] 0.128538905 1.242011e-01
## [231,] 0.130000000 1.239049e-01
## [232,] 0.130648383 1.232889e-01
## [233,] 0.130981869 1.228468e-01
## [234,] 0.131359240 1.215404e-01
## [235,] 0.133761915 1.219962e-01
## [236,] 0.133869339 1.226114e-01
## [237,] 0.134202273 1.227895e-01
## [238,] 0.134402381 1.232005e-01
## [239,] 0.134792433 1.216889e-01
## [240,] 0.134871235 1.214059e-01
## [241,] 0.135333846 1.204540e-01
## [242,] 0.135447407 1.176533e-01
## [243,] 0.136701317 1.165274e-01
## [244,] 0.139316187 1.161360e-01
## [245,] 0.140000893 1.154790e-01
## [246,] 0.140204315 1.138396e-01
## [247,] 0.140375390 1.131028e-01
## [248,] 0.140520461 1.165116e-01
## [249,] 0.140578270 1.181732e-01
## [250,] 0.141223228 1.211557e-01
## [251,] 0.142538591 1.291563e-01
## [252,] 0.143461667 1.298753e-01
## [253,] 0.144779142 1.282546e-01
## [254,] 0.145455320 1.258019e-01
## [255,] 0.145627092 1.238630e-01
## [256,] 0.145723197 1.247209e-01
## [257,] 0.145880088 1.228512e-01
## [258,] 0.147678705 1.234052e-01
## [259,] 0.148141824 1.227834e-01
## [260,] 0.148291099 1.180555e-01
## [261,] 0.148846397 1.167079e-01
## [262,] 0.149495819 1.162115e-01
## [263,] 0.151792622 1.169389e-01
## [264,] 0.153733536 1.236024e-01
## [265,] 0.154155765 1.257370e-01
## [266,] 0.155724918 1.262382e-01
## [267,] 0.160078106 1.282938e-01
## [268,] 0.160920011 1.277422e-01
## [269,] 0.161721984 1.274226e-01
## [270,] 0.164924225 1.275728e-01
## [271,] 0.165075740 1.270568e-01
## [272,] 0.165822948 1.263050e-01
## [273,] 0.165847068 1.222050e-01
## [274,] 0.167039666 1.222707e-01
## [275,] 0.167377567 1.184289e-01
## [276,] 0.169189243 1.180886e-01
## [277,] 0.170472872 1.195615e-01
## [278,] 0.171026314 1.140779e-01
## [279,] 0.171354165 1.140657e-01
## [280,] 0.171421265 1.142153e-01
## [281,] 0.172046505 1.202375e-01
## [282,] 0.172154727 1.230008e-01
## [283,] 0.177545065 1.283057e-01
## [284,] 0.180017360 1.393743e-01
## [285,] 0.181176709 1.434686e-01
## [286,] 0.182608872 1.440862e-01
## [287,] 0.184361059 1.450162e-01
## [288,] 0.185326738 1.443107e-01
## [289,] 0.187235814 1.448591e-01
## [290,] 0.189423467 1.464074e-01
## [291,] 0.193124960 1.457265e-01
## [292,] 0.193287998 1.419268e-01
## [293,] 0.197689782 1.386892e-01
## [294,] 0.200124961 1.377101e-01
## [295,] 0.208583916 1.356015e-01
## [296,] 0.211733913 1.355028e-01
## [297,] 0.214683488 1.371308e-01
## [298,] 0.215195260 1.373521e-01
## [299,] 0.221317080 1.359459e-01
## [300,] 0.221472346 1.360027e-01
## [301,] 0.227705951 1.357827e-01
## [302,] 0.229907046 1.334352e-01
## [303,] 0.234534113 1.324864e-01
## [304,] 0.238227307 1.285400e-01
## [305,] 0.240881714 1.230406e-01
## [306,] 0.243507700 1.177407e-01
## [307,] 0.245538184 1.131470e-01
## [308,] 0.245728000 1.105467e-01
## [309,] 0.252666282 1.115192e-01
## [310,] 0.255141627 1.067688e-01
## [311,] 0.255970701 1.029059e-01
## [312,] 0.256048823 1.025725e-01
## [313,] 0.258677405 9.937900e-02
## [314,] 0.259108568 9.925250e-02
## [315,] 0.264756492 9.649525e-02
## [316,] 0.271463165 8.849575e-02
## [317,] 0.273507313 8.357715e-02
## [318,] 0.274200656 8.181765e-02
## [319,] 0.277477927 6.861526e-02
## [320,] 0.285273991 6.152571e-02
## [321,] 0.290924818 6.104174e-02
## [322,] 0.291686476 6.081232e-02
## [323,] 0.297793553 5.954309e-02
## [324,] 0.334570247 5.539550e-02
## [325,] 0.365815527 4.127402e-02
## [326,] 0.372013441 4.141517e-02
## [327,] 0.403886123 4.311658e-02
## [328,] 0.433159613 4.477267e-02
## [329,] 0.481923230 4.553141e-02
## [330,] 0.482566317 5.131291e-02
## [331,] 0.503791872 5.379601e-02
## [332,] 0.514796319 4.542341e-02
## [333,] 0.541742790 4.960164e-02
## [334,] 0.553754458 4.899256e-02
## [335,] 0.589091674 4.811889e-02
## [336,] 0.780688959 4.183992e-02
## [337,] 0.927340822 3.622333e-02
## [338,] 0.954564822 3.314736e-02
## [1] 0.000000e+00 1.239388e-07 1.777073e-06 1.989397e-06 2.163292e-06
## [6] 2.606362e-06 2.663417e-06 2.719271e-06 3.363886e-06 4.237974e-06
## [11] 6.847673e-06 8.687764e-06 1.009928e-05 1.075566e-05 1.400731e-05
## [16] 1.453999e-05 1.546458e-05 1.832629e-05 1.836505e-05 1.846620e-05
## [21] 1.900402e-05 1.904403e-05 2.072256e-05 2.165181e-05 2.389255e-05
## [26] 2.951335e-05 3.081556e-05 3.919663e-05 4.257542e-05 4.351620e-05
## [31] 4.720659e-05 4.878295e-05 5.397877e-05 6.932503e-05 7.075448e-05
## [36] 7.297304e-05 8.053726e-05 8.932586e-05 9.894758e-05 1.000144e-04
## [41] 1.034820e-04 1.057415e-04 1.174689e-04 1.202161e-04 1.243010e-04
## [46] 1.316958e-04 1.323401e-04 1.378910e-04 1.384315e-04 1.397723e-04
## [51] 1.444679e-04 1.452886e-04 1.501902e-04 1.513209e-04 1.564234e-04
## [56] 1.582807e-04 1.659658e-04 1.677662e-04 1.719678e-04 1.741575e-04
## [61] 1.803757e-04 1.910092e-04 1.933805e-04 1.973330e-04 2.171164e-04
## [66] 2.182968e-04 2.316741e-04 2.488440e-04 2.619285e-04 2.640971e-04
## [71] 2.793528e-04 2.793528e-04 2.982665e-04 3.143336e-04 3.237991e-04
## [76] 3.248600e-04 3.274774e-04 3.367856e-04 3.370570e-04 3.469428e-04
## [81] 3.598786e-04 3.673770e-04 3.707869e-04 3.784538e-04 3.791920e-04
## [86] 3.822240e-04 4.076553e-04 4.078931e-04 4.106850e-04 4.198135e-04
## [91] 4.279959e-04 4.317306e-04 4.579567e-04 4.597546e-04 4.605255e-04
## [96] 4.750752e-04 5.071705e-04 5.290726e-04 5.506797e-04 5.588360e-04
## [101] 6.350361e-04 6.447060e-04 6.503776e-04 6.643526e-04 6.921212e-04
## [106] 7.283228e-04 7.283228e-04 7.471458e-04 7.557416e-04 7.557416e-04
## [111] 7.610189e-04 7.828557e-04 8.020502e-04 8.152642e-04 8.179094e-04
## [116] 8.203292e-04 8.463181e-04 8.572285e-04 8.792227e-04 9.020160e-04
## [121] 9.124876e-04 9.140590e-04 9.284303e-04 9.566255e-04 9.575722e-04
## [126] 9.733166e-04 1.004175e-03 1.028137e-03 1.076199e-03 1.092147e-03
## [131] 1.098411e-03 1.122215e-03 1.157263e-03 1.167020e-03 1.210022e-03
## [136] 1.211037e-03 1.256567e-03 1.272799e-03 1.298750e-03 1.303613e-03
## [141] 1.320979e-03 1.339276e-03 1.357373e-03 1.358782e-03 1.358782e-03
## [146] 1.361844e-03 1.397868e-03 1.405549e-03 1.412108e-03 1.434202e-03
## [151] 1.483229e-03 1.538427e-03 1.546490e-03 1.602908e-03 1.602908e-03
## [156] 1.707637e-03 1.800493e-03 1.806511e-03 1.811276e-03 1.836921e-03
## [161] 1.944382e-03 1.972148e-03 2.013140e-03 2.084965e-03 2.094750e-03
## [166] 2.108920e-03 2.161401e-03 2.187565e-03 2.277706e-03 2.322425e-03
## [171] 2.366629e-03 2.379658e-03 2.416329e-03 2.518834e-03 2.575403e-03
## [176] 2.629347e-03 2.653624e-03 2.778003e-03 2.814702e-03 2.821963e-03
## [181] 2.916565e-03 2.926430e-03 3.068838e-03 3.097115e-03 3.229226e-03
## [186] 3.233614e-03 3.235368e-03 3.263003e-03 3.274285e-03 3.336970e-03
## [191] 3.366155e-03 3.424125e-03 3.496604e-03 3.506894e-03 3.611627e-03
## [196] 3.658319e-03 3.676212e-03 3.736416e-03 3.759101e-03 3.820079e-03
## [201] 3.867399e-03 3.984070e-03 4.056705e-03 4.116633e-03 4.151456e-03
## [206] 4.165554e-03 4.253232e-03 4.349885e-03 4.349885e-03 4.372056e-03
## [211] 4.401003e-03 4.460370e-03 4.462432e-03 4.546368e-03 4.546368e-03
## [216] 4.546754e-03 4.669400e-03 4.711984e-03 4.808173e-03 4.835880e-03
## [221] 4.876885e-03 5.094065e-03 5.129181e-03 5.143298e-03 5.211144e-03
## [226] 5.241116e-03 5.241116e-03 5.346863e-03 5.403152e-03 5.424907e-03
## [231] 5.605944e-03 5.685883e-03 5.726850e-03 5.772716e-03 6.065833e-03
## [236] 6.079005e-03 6.119886e-03 6.144539e-03 6.192004e-03 6.201571e-03
## [241] 6.257294e-03 6.270655e-03 6.416770e-03 6.720451e-03 6.799520e-03
## [246] 6.822677e-03 6.842026e-03 6.858929e-03 6.865760e-03 6.943901e-03
## [251] 7.113788e-03 7.233673e-03 7.402645e-03 7.487710e-03 7.508986e-03
## [256] 7.520972e-03 7.540246e-03 7.762205e-03 7.819068e-03 7.836691e-03
## [261] 7.901499e-03 7.976969e-03 8.245555e-03 8.485456e-03 8.538546e-03
## [266] 8.736633e-03 9.295120e-03 9.402667e-03 9.504856e-03 9.913375e-03
## [271] 9.932626e-03 1.002700e-02 1.002995e-02 1.017577e-02 1.021579e-02
## [276] 1.042973e-02 1.058320e-02 1.064633e-02 1.068373e-02 1.069139e-02
## [281] 1.076657e-02 1.077988e-02 1.147149e-02 1.181607e-02 1.198240e-02
## [286] 1.218875e-02 1.244285e-02 1.258221e-02 1.285875e-02 1.317904e-02
## [291] 1.371845e-02 1.374159e-02 1.435207e-02 1.468742e-02 1.583446e-02
## [296] 1.626130e-02 1.666577e-02 1.673607e-02 1.756830e-02 1.758942e-02
## [301] 1.843584e-02 1.872954e-02 1.934256e-02 1.981729e-02 2.014389e-02
## [306] 2.045307e-02 2.068281e-02 2.070380e-02 2.147755e-02 2.174184e-02
## [311] 2.182716e-02 2.183517e-02 2.209639e-02 2.213919e-02 2.268419e-02
## [316] 2.327770e-02 2.344854e-02 2.350527e-02 2.373014e-02 2.420980e-02
## [321] 2.455474e-02 2.460105e-02 2.496469e-02 2.700195e-02 2.829157e-02
## [326] 2.854826e-02 2.992250e-02 3.123315e-02 3.345343e-02 3.348643e-02
## [331] 3.462828e-02 3.512814e-02 3.646473e-02 3.705321e-02 3.875360e-02
## [336] 4.677001e-02 5.208223e-02 5.298463e-02
## alpha area
## 1 0.006403124 0.000000e+00
## 2 0.011000000 1.239388e-07
## 3 0.026500000 1.777073e-06
## 4 0.027856777 1.989397e-06
## 5 0.028792360 2.163292e-06
## 6 0.030500000 2.606362e-06
p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)# Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)geom_indicesc <- indice1$results[[2]]$geom_indices
geom_indicescmenosr <- indice2$results[[2]]$geom_indices
geom_indicescmasr <- indice3$results[[2]]$geom_indices
geom_indicescmenosr2 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicescmasr2 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicesc$label <- "centros"
geom_indicescmenosr$label <- "centros menos rangos"
geom_indicescmasr$label <- "centros más rangos"
data_combined <- rbind(geom_indicesc,geom_indicescmenosr,geom_indicescmasr)
data_combined1 <- rbind(geom_indicescmenosr2, geom_indicescmasr2)
data_combined1 <- rbind(c(0,1),data_combined1)
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica con datos uniformes",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))alpha.vals <- sort(unique(c(geom_indicescmenosr2$alpha, geom_indicescmasr2$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr2$alpha, geom_indicescmasr2$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr2$alpha, geom_indicescmenosr2$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
table.diff <- cbind(alpha.vals, diff.geom_corr)
table.diff## alpha.vals diff.geom_corr
## [1,] 0.02018044 4.919256e-05
## [2,] 0.02147091 1.394103e-04
## [3,] 0.02470324 2.100808e-04
## [4,] 0.02540177 2.195322e-04
## [5,] 0.02692582 2.253926e-04
## [6,] 0.03041381 4.998547e-04
## [7,] 0.03376759 5.530796e-04
## [8,] 0.03579455 7.499706e-04
## [9,] 0.03946201 9.730748e-04
## [10,] 0.03992493 1.060742e-03
## [11,] 0.04200000 1.391576e-03
## [12,] 0.04294182 1.588818e-03
## [13,] 0.04382921 1.615168e-03
## [14,] 0.04810405 1.708986e-03
## [15,] 0.05001000 1.731744e-03
## [16,] 0.05020956 1.478886e-03
## [17,] 0.05093133 1.325416e-03
## [18,] 0.05380753 1.364250e-03
## [19,] 0.05749130 1.795422e-03
## [20,] 0.05996040 2.068730e-03
## [21,] 0.06067125 2.487251e-03
## [22,] 0.06250000 3.165127e-03
## [23,] 0.06280127 3.263559e-03
## [24,] 0.06280127 5.188203e-03
## [25,] 0.06469351 5.481444e-03
## [26,] 0.06469351 5.481444e-03
## [27,] 0.06470896 6.919279e-03
## [28,] 0.06719561 7.827879e-03
## [29,] 0.07011419 8.022038e-03
## [30,] 0.07097359 9.873732e-03
## [31,] 0.07102112 9.976035e-03
## [32,] 0.07180007 1.215710e-02
## [33,] 0.07294004 1.266270e-02
## [34,] 0.07426473 1.414962e-02
## [35,] 0.07432362 1.616300e-02
## [36,] 0.07544700 1.739761e-02
## [37,] 0.07566538 1.743813e-02
## [38,] 0.07615773 1.674220e-02
## [39,] 0.07788453 1.662443e-02
## [40,] 0.07826238 1.663864e-02
## [41,] 0.07864636 1.666709e-02
## [42,] 0.08062258 1.690682e-02
## [43,] 0.08062258 1.814581e-02
## [44,] 0.08068612 1.877362e-02
## [45,] 0.08095678 2.097067e-02
## [46,] 0.08137721 2.266459e-02
## [47,] 0.08139410 2.415320e-02
## [48,] 0.08139410 2.415320e-02
## [49,] 0.08231191 2.518693e-02
## [50,] 0.08271034 2.739085e-02
## [51,] 0.08276473 2.769444e-02
## [52,] 0.08341013 2.885954e-02
## [53,] 0.08403719 3.039848e-02
## [54,] 0.08403719 3.039848e-02
## [55,] 0.08509407 3.123306e-02
## [56,] 0.08575547 3.248788e-02
## [57,] 0.08597819 3.261806e-02
## [58,] 0.08608281 3.328947e-02
## [59,] 0.08640168 3.338397e-02
## [60,] 0.08703591 3.444838e-02
## [61,] 0.08914034 3.945706e-02
## [62,] 0.08995693 4.061082e-02
## [63,] 0.09024411 4.101159e-02
## [64,] 0.09055385 4.139006e-02
## [65,] 0.09058835 4.795386e-02
## [66,] 0.09073175 4.898471e-02
## [67,] 0.09106179 5.183673e-02
## [68,] 0.09150000 5.398139e-02
## [69,] 0.09178780 5.496530e-02
## [70,] 0.09212627 5.742675e-02
## [71,] 0.09222391 5.904757e-02
## [72,] 0.09222391 5.904757e-02
## [73,] 0.09222391 6.107897e-02
## [74,] 0.09250541 6.045016e-02
## [75,] 0.09257564 5.944555e-02
## [76,] 0.09388956 5.999833e-02
## [77,] 0.09396276 6.173392e-02
## [78,] 0.09406912 6.477898e-02
## [79,] 0.09501184 6.549232e-02
## [80,] 0.09502105 6.970401e-02
## [81,] 0.09512623 7.694608e-02
## [82,] 0.09529428 7.752185e-02
## [83,] 0.09552487 7.693440e-02
## [84,] 0.09552487 7.693440e-02
## [85,] 0.09602213 7.950099e-02
## [86,] 0.09604166 8.211761e-02
## [87,] 0.09610411 8.397357e-02
## [88,] 0.09688137 8.508498e-02
## [89,] 0.09688137 8.474484e-02
## [90,] 0.09740252 8.600927e-02
## [91,] 0.09947487 8.601274e-02
## [92,] 0.09963559 8.530374e-02
## [93,] 0.09964437 8.336546e-02
## [94,] 0.09972963 8.336838e-02
## [95,] 0.10003125 8.469580e-02
## [96,] 0.10040418 8.611032e-02
## [97,] 0.10099629 8.833390e-02
## [98,] 0.10162308 9.059248e-02
## [99,] 0.10376536 9.276340e-02
## [100,] 0.10404326 9.273975e-02
## [101,] 0.10490591 9.606294e-02
## [102,] 0.10491544 9.792412e-02
## [103,] 0.10550474 9.862591e-02
## [104,] 0.10597287 9.983893e-02
## [105,] 0.10680005 1.019116e-01
## [106,] 0.10705606 1.051056e-01
## [107,] 0.10707007 1.094392e-01
## [108,] 0.10717859 1.095037e-01
## [109,] 0.10748953 1.090238e-01
## [110,] 0.10770330 1.087560e-01
## [111,] 0.10925200 1.086987e-01
## [112,] 0.10965856 1.126944e-01
## [113,] 0.11007270 1.135705e-01
## [114,] 0.11032792 1.123080e-01
## [115,] 0.11059950 1.114310e-01
## [116,] 0.11114068 1.126297e-01
## [117,] 0.11115417 1.195108e-01
## [118,] 0.11115417 1.195108e-01
## [119,] 0.11115755 1.223201e-01
## [120,] 0.11144954 1.227990e-01
## [121,] 0.11171504 1.224438e-01
## [122,] 0.11285943 1.223696e-01
## [123,] 0.11289818 1.224085e-01
## [124,] 0.11294357 1.256227e-01
## [125,] 0.11352973 1.280682e-01
## [126,] 0.11352973 1.299463e-01
## [127,] 0.11362328 1.344886e-01
## [128,] 0.11450000 1.396632e-01
## [129,] 0.11461239 1.398864e-01
## [130,] 0.11503912 1.389452e-01
## [131,] 0.11505325 1.388692e-01
## [132,] 0.11536464 1.369707e-01
## [133,] 0.11600539 1.374506e-01
## [134,] 0.11706942 1.419089e-01
## [135,] 0.11718042 1.430348e-01
## [136,] 0.11737653 1.445742e-01
## [137,] 0.11766053 1.450505e-01
## [138,] 0.11830152 1.469967e-01
## [139,] 0.11884864 1.501798e-01
## [140,] 0.11884969 1.501841e-01
## [141,] 0.11950418 1.509076e-01
## [142,] 0.11954183 1.507008e-01
## [143,] 0.11954183 1.528149e-01
## [144,] 0.11992081 1.518710e-01
## [145,] 0.11992081 1.518710e-01
## [146,] 0.12014991 1.499386e-01
## [147,] 0.12062442 1.546599e-01
## [148,] 0.12091733 1.637870e-01
## [149,] 0.12110326 1.686469e-01
## [150,] 0.12116621 1.688479e-01
## [151,] 0.12159770 1.700020e-01
## [152,] 0.12320816 1.755256e-01
## [153,] 0.12582230 1.772603e-01
## [154,] 0.12617845 1.772334e-01
## [155,] 0.12683552 1.796901e-01
## [156,] 0.12709839 1.795788e-01
## [157,] 0.12731457 1.805167e-01
## [158,] 0.12863126 1.865692e-01
## [159,] 0.12884487 1.926452e-01
## [160,] 0.12887591 1.930692e-01
## [161,] 0.12955308 2.011726e-01
## [162,] 0.13001538 2.029986e-01
## [163,] 0.13086252 2.048001e-01
## [164,] 0.13148764 2.082297e-01
## [165,] 0.13449535 2.088702e-01
## [166,] 0.13487123 2.131522e-01
## [167,] 0.13520817 2.197060e-01
## [168,] 0.13686581 2.215034e-01
## [169,] 0.13845216 2.224939e-01
## [170,] 0.13926952 2.232911e-01
## [171,] 0.14010799 2.232295e-01
## [172,] 0.14020075 2.258723e-01
## [173,] 0.14058449 2.320001e-01
## [174,] 0.14074889 2.326391e-01
## [175,] 0.14188464 2.349743e-01
## [176,] 0.14244385 2.348190e-01
## [177,] 0.14302447 2.336573e-01
## [178,] 0.14317821 2.322750e-01
## [179,] 0.14350000 2.299976e-01
## [180,] 0.14534442 2.318852e-01
## [181,] 0.14536936 2.306065e-01
## [182,] 0.14547251 2.308320e-01
## [183,] 0.14560220 2.320255e-01
## [184,] 0.14630875 2.377558e-01
## [185,] 0.14760505 2.415665e-01
## [186,] 0.14767871 2.417721e-01
## [187,] 0.14869095 2.437890e-01
## [188,] 0.14869095 2.437890e-01
## [189,] 0.14894966 2.448573e-01
## [190,] 0.14920121 2.452614e-01
## [191,] 0.14938290 2.464485e-01
## [192,] 0.14949582 2.440425e-01
## [193,] 0.14985410 2.483663e-01
## [194,] 0.15138444 2.496590e-01
## [195,] 0.15182226 2.500014e-01
## [196,] 0.15277516 2.519946e-01
## [197,] 0.15289621 2.520702e-01
## [198,] 0.15344706 2.507843e-01
## [199,] 0.15367498 2.481009e-01
## [200,] 0.15435349 2.473548e-01
## [201,] 0.15502016 2.474313e-01
## [202,] 0.15598477 2.453247e-01
## [203,] 0.15598477 2.453247e-01
## [204,] 0.15601602 2.460062e-01
## [205,] 0.15609372 2.434505e-01
## [206,] 0.15616017 2.398296e-01
## [207,] 0.15741982 2.371856e-01
## [208,] 0.15879310 2.362606e-01
## [209,] 0.15959402 2.337385e-01
## [210,] 0.16058954 2.335908e-01
## [211,] 0.16070159 2.458281e-01
## [212,] 0.16082288 2.488522e-01
## [213,] 0.16095419 2.518737e-01
## [214,] 0.16155494 2.537051e-01
## [215,] 0.16233915 2.577380e-01
## [216,] 0.16363145 2.631303e-01
## [217,] 0.16368873 2.696814e-01
## [218,] 0.16394283 2.724671e-01
## [219,] 0.16426275 2.761380e-01
## [220,] 0.16573774 2.829839e-01
## [221,] 0.16580184 2.824567e-01
## [222,] 0.16604292 2.822955e-01
## [223,] 0.16648123 2.912974e-01
## [224,] 0.16648123 2.912974e-01
## [225,] 0.16680003 2.905927e-01
## [226,] 0.16714066 2.910083e-01
## [227,] 0.16770510 3.101936e-01
## [228,] 0.16905990 3.113911e-01
## [229,] 0.16918924 3.087431e-01
## [230,] 0.17023807 3.080962e-01
## [231,] 0.17110596 3.081846e-01
## [232,] 0.17133374 3.039878e-01
## [233,] 0.17154008 3.038384e-01
## [234,] 0.17270206 3.044840e-01
## [235,] 0.17278961 3.048619e-01
## [236,] 0.17300000 3.016985e-01
## [237,] 0.17372680 3.020123e-01
## [238,] 0.17397126 3.034359e-01
## [239,] 0.17439968 3.010583e-01
## [240,] 0.17507141 3.083450e-01
## [241,] 0.17534537 3.081362e-01
## [242,] 0.17560182 3.058329e-01
## [243,] 0.17570501 2.986868e-01
## [244,] 0.17613915 2.941528e-01
## [245,] 0.18027756 2.976820e-01
## [246,] 0.18140080 2.976922e-01
## [247,] 0.18337121 2.978874e-01
## [248,] 0.18501689 3.032793e-01
## [249,] 0.18577944 3.043794e-01
## [250,] 0.18988483 3.089282e-01
## [251,] 0.19006578 3.087606e-01
## [252,] 0.19006578 3.227233e-01
## [253,] 0.19012890 3.235793e-01
## [254,] 0.19248441 3.194467e-01
## [255,] 0.19262918 3.187050e-01
## [256,] 0.19420929 3.177654e-01
## [257,] 0.19450964 3.145903e-01
## [258,] 0.19641092 3.146421e-01
## [259,] 0.19724604 3.156191e-01
## [260,] 0.20238824 3.308225e-01
## [261,] 0.20300000 3.289667e-01
## [262,] 0.20376518 3.267585e-01
## [263,] 0.20504938 3.293686e-01
## [264,] 0.20535092 3.294390e-01
## [265,] 0.20706038 3.373548e-01
## [266,] 0.20885641 3.357059e-01
## [267,] 0.20892582 3.333070e-01
## [268,] 0.20898624 3.286790e-01
## [269,] 0.20967177 3.244824e-01
## [270,] 0.21120192 3.099635e-01
## [271,] 0.21128417 3.062090e-01
## [272,] 0.21239645 3.026674e-01
## [273,] 0.21425744 3.016912e-01
## [274,] 0.21543038 3.035848e-01
## [275,] 0.21739423 3.026389e-01
## [276,] 0.21777339 2.935779e-01
## [277,] 0.22754175 2.947128e-01
## [278,] 0.22808113 2.996534e-01
## [279,] 0.22886950 3.066391e-01
## [280,] 0.23005434 3.178645e-01
## [281,] 0.23325362 3.161881e-01
## [282,] 0.23505797 3.131822e-01
## [283,] 0.23992134 3.073737e-01
## [284,] 0.24000833 2.968684e-01
## [285,] 0.24748737 2.936062e-01
## [286,] 0.25519649 2.908013e-01
## [287,] 0.25640008 2.741962e-01
## [288,] 0.25870302 2.649559e-01
## [289,] 0.26054030 2.593866e-01
## [290,] 0.26160275 2.561339e-01
## [291,] 0.26288020 2.505048e-01
## [292,] 0.26454725 2.394784e-01
## [293,] 0.26622782 2.338800e-01
## [294,] 0.26864289 2.240522e-01
## [295,] 0.27280213 2.156415e-01
## [296,] 0.27436108 2.101475e-01
## [297,] 0.28925292 1.903975e-01
## [298,] 0.29054303 1.761821e-01
## [299,] 0.29610007 1.748734e-01
## [300,] 0.29610007 1.748734e-01
## [301,] 0.29618786 1.708443e-01
## [302,] 0.29763904 1.686579e-01
## [303,] 0.29769951 1.643059e-01
## [304,] 0.31329738 1.593809e-01
## [305,] 0.31715769 1.527778e-01
## [306,] 0.31715769 1.527778e-01
## [307,] 0.33568177 1.537926e-01
## [308,] 0.33864768 1.492265e-01
## [309,] 0.33915925 1.506474e-01
## [310,] 0.34033219 1.557826e-01
## [311,] 0.37955369 1.521600e-01
## [312,] 0.38527555 1.506996e-01
## [313,] 0.39300922 1.481949e-01
## [314,] 0.39395431 1.385102e-01
## [315,] 0.41270449 1.338462e-01
## [316,] 0.41831687 1.250355e-01
## [317,] 0.43229880 1.185509e-01
## [318,] 0.45262595 1.087905e-01
## [319,] 0.51032857 9.506492e-02
## [320,] 0.52236099 8.787769e-02
## [321,] 0.52259832 8.774719e-02
## [322,] 0.55148640 8.408755e-02
## [323,] 0.55381315 8.410634e-02
## [324,] 0.57747381 1.024165e-01
## [325,] 0.60609178 1.001165e-01
## [326,] 0.63496535 9.949764e-02
## [327,] 0.90067044 5.853768e-02
## [1] 0.000000e+00 1.799054e-07 8.589554e-07 1.012306e-06 1.355816e-06
## [6] 3.099304e-06 4.954208e-06 6.474372e-06 1.004308e-05 1.053412e-05
## [11] 1.342174e-05 1.491812e-05 1.635141e-05 2.365705e-05 2.695766e-05
## [16] 2.725279e-05 2.820943e-05 3.213329e-05 3.874722e-05 4.385512e-05
## [21] 4.562316e-05 5.141140e-05 5.239463e-05 5.239463e-05 6.276681e-05
## [26] 6.276681e-05 6.287375e-05 8.233891e-05 1.057519e-04 1.142373e-04
## [31] 1.147115e-04 1.241813e-04 1.386164e-04 1.573602e-04 1.583120e-04
## [36] 1.778562e-04 1.816644e-04 1.899074e-04 2.186144e-04 2.249013e-04
## [41] 2.313012e-04 2.647127e-04 2.647127e-04 2.659056e-04 2.715815e-04
## [46] 2.811104e-04 2.815185e-04 2.815185e-04 3.046351e-04 3.155485e-04
## [51] 3.170548e-04 3.356808e-04 3.547426e-04 3.547426e-04 3.877519e-04
## [56] 4.092394e-04 4.165044e-04 4.199870e-04 4.306321e-04 4.524804e-04
## [61] 5.355149e-04 5.686775e-04 5.804552e-04 5.932752e-04 5.949298e-04
## [66] 6.019539e-04 6.190623e-04 6.427174e-04 6.585363e-04 6.779737e-04
## [71] 6.837392e-04 6.837392e-04 6.837392e-04 7.007554e-04 7.049309e-04
## [76] 7.837638e-04 7.882824e-04 7.951726e-04 8.569134e-04 8.575553e-04
## [81] 8.656486e-04 8.786761e-04 8.964160e-04 8.964160e-04 9.359492e-04
## [86] 9.375526e-04 9.427969e-04 1.008930e-03 1.008930e-03 1.053753e-03
## [91] 1.232002e-03 1.245712e-03 1.246444e-03 1.253553e-03 1.279098e-03
## [96] 1.311212e-03 1.363514e-03 1.420297e-03 1.619022e-03 1.644795e-03
## [101] 1.727663e-03 1.728597e-03 1.786717e-03 1.833455e-03 1.917753e-03
## [106] 1.944662e-03 1.946195e-03 1.958078e-03 1.991979e-03 2.015227e-03
## [111] 2.183569e-03 2.229386e-03 2.276420e-03 2.305083e-03 2.335346e-03
## [116] 2.396298e-03 2.397911e-03 2.397911e-03 2.398324e-03 2.434180e-03
## [121] 2.466689e-03 2.606727e-03 2.611471e-03 2.617173e-03 2.692242e-03
## [126] 2.692242e-03 2.704823e-03 2.827268e-03 2.842990e-03 2.902283e-03
## [131] 2.904244e-03 2.946896e-03 3.034967e-03 3.185963e-03 3.201839e-03
## [136] 3.230192e-03 3.271386e-03 3.365610e-03 3.447776e-03 3.447934e-03
## [141] 3.546702e-03 3.552376e-03 3.552376e-03 3.609931e-03 3.609931e-03
## [146] 3.644281e-03 3.717669e-03 3.765644e-03 3.797001e-03 3.807630e-03
## [151] 3.880984e-03 4.163661e-03 4.627044e-03 4.690165e-03 4.808236e-03
## [156] 4.855441e-03 4.894465e-03 5.140118e-03 5.181270e-03 5.187263e-03
## [161] 5.323490e-03 5.417338e-03 5.590832e-03 5.721000e-03 6.349222e-03
## [166] 6.429342e-03 6.503369e-03 6.870541e-03 7.223494e-03 7.406004e-03
## [171] 7.593176e-03 7.614127e-03 7.703156e-03 7.741400e-03 8.008272e-03
## [176] 8.139585e-03 8.275252e-03 8.310962e-03 8.384973e-03 8.812666e-03
## [181] 8.818417e-03 8.842227e-03 8.872319e-03 9.040305e-03 9.353448e-03
## [186] 9.371256e-03 9.618031e-03 9.618031e-03 9.681376e-03 9.743072e-03
## [191] 9.787849e-03 9.815407e-03 9.904391e-03 1.028646e-02 1.039591e-02
## [196] 1.063604e-02 1.066655e-02 1.080469e-02 1.086124e-02 1.102907e-02
## [201] 1.119403e-02 1.143067e-02 1.143067e-02 1.143836e-02 1.145728e-02
## [206] 1.147321e-02 1.177198e-02 1.209644e-02 1.228364e-02 1.251618e-02
## [211] 1.254373e-02 1.257391e-02 1.260699e-02 1.275940e-02 1.296152e-02
## [216] 1.330156e-02 1.331701e-02 1.338624e-02 1.347459e-02 1.389199e-02
## [221] 1.391009e-02 1.397815e-02 1.410583e-02 1.410583e-02 1.419847e-02
## [226] 1.429759e-02 1.447268e-02 1.489455e-02 1.493449e-02 1.525762e-02
## [231] 1.552510e-02 1.559434e-02 1.565703e-02 1.601083e-02 1.603753e-02
## [236] 1.610100e-02 1.632050e-02 1.639468e-02 1.652366e-02 1.673079e-02
## [241] 1.681520e-02 1.689363e-02 1.692445e-02 1.705216e-02 1.828409e-02
## [246] 1.861847e-02 1.920543e-02 1.970453e-02 1.993663e-02 2.120490e-02
## [251] 2.126077e-02 2.126077e-02 2.128120e-02 2.203366e-02 2.207980e-02
## [256] 2.258190e-02 2.267639e-02 2.327461e-02 2.353819e-02 2.523935e-02
## [261] 2.544060e-02 2.569063e-02 2.611360e-02 2.621294e-02 2.678963e-02
## [266] 2.739257e-02 2.741571e-02 2.743557e-02 2.765801e-02 2.813230e-02
## [271] 2.815748e-02 2.849413e-02 2.905558e-02 2.941167e-02 3.000600e-02
## [276] 3.011732e-02 3.299618e-02 3.315780e-02 3.339955e-02 3.377617e-02
## [281] 3.478774e-02 3.535283e-02 3.684770e-02 3.687353e-02 3.906942e-02
## [286] 4.131124e-02 4.164126e-02 4.225144e-02 4.272801e-02 4.300014e-02
## [291] 4.332014e-02 4.371937e-02 4.411242e-02 4.465352e-02 4.555042e-02
## [296] 4.587803e-02 4.871340e-02 4.894070e-02 4.991248e-02 4.991248e-02
## [301] 4.992748e-02 5.017223e-02 5.018216e-02 5.266817e-02 5.325794e-02
## [306] 5.325794e-02 5.610680e-02 5.654939e-02 5.662646e-02 5.680918e-02
## [311] 6.277713e-02 6.363941e-02 6.478550e-02 6.491641e-02 6.742605e-02
## [316] 6.812779e-02 6.978536e-02 7.199676e-02 7.748226e-02 7.853964e-02
## [321] 7.856046e-02 8.098959e-02 8.118529e-02 8.360853e-02 8.647366e-02
## [326] 8.934651e-02 1.049003e-01
## alpha area
## 1 0.02018044 0.000000e+00
## 2 0.02147091 1.799054e-07
## 3 0.02470324 8.589554e-07
## 4 0.02540177 1.012306e-06
## 5 0.02692582 1.355816e-06
## 6 0.03041381 3.099304e-06
p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)# Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)geom_indicesc <- indice1$results[[3]]$geom_indices
geom_indicescmenosr <- indice2$results[[3]]$geom_indices
geom_indicescmasr <- indice3$results[[3]]$geom_indices
geom_indicescmenosr3 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicescmasr3 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicesc$label <- "centros"
geom_indicescmenosr$label <- "centros menos rangos"
geom_indicescmasr$label <- "centros más rangos"
data_combined <- rbind(geom_indicesc,geom_indicescmenosr,geom_indicescmasr)
data_combined1 <- rbind(geom_indicescmenosr3, geom_indicescmasr3)
data_combined1 <- rbind(c(0,1),data_combined1)
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica con datos uniformes",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))alpha.vals <- sort(unique(c(geom_indicescmenosr3$alpha, geom_indicescmasr3$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr3$alpha, geom_indicescmasr3$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr3$alpha, geom_indicescmenosr3$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
table.diff <- cbind(alpha.vals, diff.geom_corr)
table.diff## alpha.vals diff.geom_corr
## [1,] 0.02385372 -1.137416e-05
## [2,] 0.03003748 9.290018e-05
## [3,] 0.03067572 1.073896e-04
## [4,] 0.03297347 3.250368e-05
## [5,] 0.04162031 2.319776e-06
## [6,] 0.04215744 2.058668e-04
## [7,] 0.04350000 5.651306e-04
## [8,] 0.04509989 7.734447e-04
## [9,] 0.04674666 9.189586e-04
## [10,] 0.04743416 9.468998e-04
## [11,] 0.04950000 9.512227e-04
## [12,] 0.04952020 9.556540e-04
## [13,] 0.05203124 1.656691e-03
## [14,] 0.05246189 1.749880e-03
## [15,] 0.05622277 1.909513e-03
## [16,] 0.05749130 1.599704e-03
## [17,] 0.05771698 2.163694e-03
## [18,] 0.05771698 2.163694e-03
## [19,] 0.05983519 2.451452e-03
## [20,] 0.05993538 2.461262e-03
## [21,] 0.06033448 2.601503e-03
## [22,] 0.06039247 2.284531e-03
## [23,] 0.06058259 2.250746e-03
## [24,] 0.06222741 2.714737e-03
## [25,] 0.06313478 2.802143e-03
## [26,] 0.06313478 2.802143e-03
## [27,] 0.06403124 3.514350e-03
## [28,] 0.06403124 4.167198e-03
## [29,] 0.06462198 4.632111e-03
## [30,] 0.06519394 4.597367e-03
## [31,] 0.06768309 5.057402e-03
## [32,] 0.06964194 5.351024e-03
## [33,] 0.07008745 6.223468e-03
## [34,] 0.07156116 6.751861e-03
## [35,] 0.07280110 6.702415e-03
## [36,] 0.07323933 6.726773e-03
## [37,] 0.07354590 7.757023e-03
## [38,] 0.07354590 7.757023e-03
## [39,] 0.07396114 8.749376e-03
## [40,] 0.07500000 9.650222e-03
## [41,] 0.07514819 1.075108e-02
## [42,] 0.08009994 1.274172e-02
## [43,] 0.08062258 1.518284e-02
## [44,] 0.08077747 1.576390e-02
## [45,] 0.08095678 1.681115e-02
## [46,] 0.08158431 1.873112e-02
## [47,] 0.08193900 2.014492e-02
## [48,] 0.08193900 2.014492e-02
## [49,] 0.08255453 2.245282e-02
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## [281] 4.686940e-02 4.698820e-02 4.894246e-02 4.936891e-02 5.050060e-02
## [286] 5.082171e-02 5.148223e-02 5.569661e-02 5.590173e-02 5.809315e-02
## [291] 6.119099e-02 6.205995e-02 6.277262e-02 6.418048e-02 6.420686e-02
## [296] 6.770398e-02 6.842913e-02 6.932205e-02 6.957119e-02 7.029937e-02
## [301] 7.109787e-02 7.395648e-02 7.412956e-02 7.562097e-02 7.571677e-02
## [306] 7.583712e-02 7.668098e-02 7.964192e-02 8.012428e-02 8.204644e-02
## [311] 8.342278e-02 8.366194e-02 8.507267e-02 8.621628e-02 8.863278e-02
## [316] 8.869267e-02 9.035778e-02 9.639460e-02 9.676138e-02 9.823824e-02
## [321] 1.001660e-01 1.087096e-01 1.107757e-01 1.382919e-01 1.574354e-01
## [326] 1.595904e-01 1.738993e-01
## alpha area
## 1 0.02385372 0.000000e+00
## 2 0.03003748 5.744720e-07
## 3 0.03067572 6.430131e-07
## 4 0.03297347 7.176984e-07
## 5 0.04162031 7.377571e-07
## 6 0.04215744 8.483355e-07
p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)# Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)n=100
cita <- round(runif(n, 0, 2*pi),2)
r1 <- round(runif(n, 3,4),2)
x1.center <- r1*cos(cita)
y1.center <- r1*sin(cita)
r2 <- round(runif(n, 6,7),2)
x2.center <- r2*cos(cita)
y2.center <- r2*sin(cita)
r3 <- round(runif(n, 10,11),2)
x3.center <- r3*cos(cita)
y3.center <- r3*sin(cita)
x1.ranks <- round(runif(n, 1, 2),2)
x2.ranks <- round(runif(n, 1, 2),2)
x3.ranks <- round(runif(n, 1, 2),2)
y1.ranks <- round(runif(n, 1, 2),2)
y2.ranks <- round(runif(n, 1, 2),2)
y3.ranks <- round(runif(n, 1, 2),2)
x1.lower <- x1.center - x1.ranks
x1.upper <- x1.center + x1.ranks
x2.lower <- x2.center - x2.ranks
x2.upper <- x2.center + x2.ranks
x3.lower <- x3.center - x3.ranks
x3.upper <- x3.center + x3.ranks
y1.lower <- y1.center - y1.ranks
y2.lower <- y2.center - y2.ranks
y3.lower <- y3.center - y3.ranks
y1.upper <- y1.center + y1.ranks
y2.upper <- y2.center + y2.ranks
y3.upper <- y3.center + y3.ranks
tabla <- data.frame(x1.lower,x1.upper,x2.lower,x2.upper,x3.lower,x3.upper,y1.lower,y1.upper,y2.lower,y2.upper,y3.lower,y3.upper, x1.center, x1.ranks,x2.center,x2.ranks,x3.center,x3.ranks, y1.center, y1.ranks, y2.center, y2.ranks, y3.center, y3.ranks)
# Primero fijamos un espacio adecuado para graficar todo
plot(NULL, xlim = c(-12, 12), ylim = c(-12, 12), xlab = "x", ylab = "y", asp = 1,
main = "Rectángulos simbólicos y sus centros")
# Dibujar los rectángulos del grupo 1
for (i in 1:n) {
rect(x1.lower[i], y1.lower[i], x1.upper[i], y1.upper[i], border = "blue", col = rgb(0, 0, 1, 0.2))
points(x1.center[i], y1.center[i], col = "blue", pch = 19, cex = 0.5)
}
# Rectángulos del grupo 2
for (i in 1:n) {
rect(x2.lower[i], y2.lower[i], x2.upper[i], y2.upper[i], border = "forestgreen", col = rgb(0, 0.6, 0, 0.2))
points(x2.center[i], y2.center[i], col = "forestgreen", pch = 19, cex = 0.5)
}
# Rectángulos del grupo 3
for (i in 1:n) {
rect(x3.lower[i], y3.lower[i], x3.upper[i], y3.upper[i], border = "darkorange", col = rgb(1, 0.5, 0, 0.2))
points(x3.center[i], y3.center[i], col = "darkorange", pch = 19, cex = 0.5)
}
legend("topright", legend = c("Grupo 1", "Grupo 2", "Grupo 3"),
col = c("blue", "forestgreen", "darkorange"), pch = 19, bty = "n")Xc <- c(x1.center, x2.center, x3.center)
Yc <- c(y1.center, y2.center, y3.center)
Xl <- c(x1.lower, x2.lower, x3.lower)
Yl <- c(y1.lower, y2.lower, y3.lower)
Xu <- c(x1.upper, x2.upper, x3.upper)
Yu <- c(y1.upper, y2.upper, y3.upper)
indice1 <- spatgeom(y=Yc, x=Xc) ## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
geom_indicesc <- indice1$results[[1]]$geom_indices
geom_indicescmenosr <- indice2$results[[1]]$geom_indices
geom_indicescmasr <- indice3$results[[1]]$geom_indices
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup()
geom_indicesc$label <- "centros"
geom_indicescmenosr$label <- "centros menos rangos"
geom_indicescmasr$label <- "centros más rangos"
data_combined <- rbind(geom_indicesc,geom_indicescmenosr,geom_indicescmasr)
data_combined1 <- rbind(geom_indicescmenosr1, geom_indicescmasr1)
data_combined1 <- rbind(c(0,1),data_combined1)
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica con datos uniformes",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))#Área acumulada entre las curvas: centros menos rangos y centros más rangos.
library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmenosr1$alpha, geom_indicescmasr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
table.diff <- cbind(alpha.vals, diff.geom_corr)
table.diff## alpha.vals diff.geom_corr
## [1,] 0.05751881 -2.851600e-06
## [2,] 0.07104237 5.034950e-06
## [3,] 0.07929438 7.526247e-06
## [4,] 0.08378608 2.194501e-05
## [5,] 0.08510697 2.372027e-05
## [6,] 0.09448835 3.604006e-05
## [7,] 0.10077100 6.265201e-05
## [8,] 0.10448809 7.549548e-05
## [9,] 0.10510004 4.892473e-05
## [10,] 0.10649516 3.917267e-05
## [11,] 0.10805732 3.290353e-05
## [12,] 0.10856909 3.214808e-05
## [13,] 0.11249304 4.123253e-05
## [14,] 0.11453900 3.933572e-05
## [15,] 0.12265966 4.131728e-05
## [16,] 0.12447487 5.746840e-05
## [17,] 0.12515969 7.608835e-05
## [18,] 0.12601046 8.300276e-05
## [19,] 0.12654086 6.456527e-05
## [20,] 0.12673707 5.706473e-05
## [21,] 0.13117561 4.395024e-05
## [22,] 0.13122643 4.271595e-05
## [23,] 0.13138331 4.195758e-05
## [24,] 0.13196605 -1.467501e-06
## [25,] 0.13347483 3.093752e-05
## [26,] 0.13487940 6.590207e-05
## [27,] 0.13666559 7.664236e-05
## [28,] 0.13698212 2.814767e-05
## [29,] 0.14108375 2.784344e-05
## [30,] 0.14204654 2.241877e-05
## [31,] 0.14513139 6.710959e-06
## [32,] 0.14578325 4.390752e-06
## [33,] 0.14819941 -4.446061e-05
## [34,] 0.14967816 -4.700484e-05
## [35,] 0.15084774 -4.429050e-05
## [36,] 0.15111533 -1.507392e-05
## [37,] 0.15588017 -2.607831e-05
## [38,] 0.15810833 -2.318253e-05
## [39,] 0.15819744 -8.852952e-05
## [40,] 0.15857712 -9.523001e-05
## [41,] 0.16026817 -1.297848e-04
## [42,] 0.16369779 -1.412181e-04
## [43,] 0.16662958 -1.457363e-04
## [44,] 0.16700944 -1.449002e-04
## [45,] 0.16758356 -1.046129e-04
## [46,] 0.17358522 -1.055145e-04
## [47,] 0.17700929 -1.635855e-04
## [48,] 0.18032854 -1.671663e-04
## [49,] 0.18355639 -1.250827e-04
## [50,] 0.18692391 -6.579081e-05
## [51,] 0.19082829 -6.216795e-05
## [52,] 0.19407528 -8.923028e-05
## [53,] 0.19527559 -9.201903e-05
## [54,] 0.19850704 -9.297855e-05
## [55,] 0.20353335 -1.051307e-04
## [56,] 0.20474455 -7.256617e-05
## [57,] 0.20558321 -5.714380e-05
## [58,] 0.20698654 -1.273881e-04
## [59,] 0.20766314 -2.073486e-04
## [60,] 0.21022676 -1.763627e-04
## [61,] 0.21143459 -1.859849e-04
## [62,] 0.21220795 -2.205882e-04
## [63,] 0.21247185 -1.422611e-04
## [64,] 0.21257656 -1.395213e-04
## [65,] 0.21306687 -1.363023e-04
## [66,] 0.21322828 -1.447408e-04
## [67,] 0.21421787 -3.008333e-04
## [68,] 0.21959770 -2.693383e-04
## [69,] 0.21963777 -2.693068e-04
## [70,] 0.22160124 -2.623153e-04
## [71,] 0.22222029 -3.322516e-04
## [72,] 0.22315787 -3.279835e-04
## [73,] 0.22368154 -2.350356e-04
## [74,] 0.22451330 -9.401331e-05
## [75,] 0.22535793 -8.600012e-05
## [76,] 0.22736342 -6.571844e-05
## [77,] 0.22785171 -5.695945e-05
## [78,] 0.23035518 -7.106645e-05
## [79,] 0.23099590 3.630833e-05
## [80,] 0.23133272 6.773882e-05
## [81,] 0.23158479 1.081890e-04
## [82,] 0.23174957 9.848564e-05
## [83,] 0.23278386 9.616329e-05
## [84,] 0.23305077 8.199702e-05
## [85,] 0.23366207 5.447681e-05
## [86,] 0.23480390 4.144262e-05
## [87,] 0.23538897 3.759687e-05
## [88,] 0.23641187 1.378654e-05
## [89,] 0.23678760 -8.729911e-05
## [90,] 0.23685015 -1.502433e-04
## [91,] 0.23685968 -2.076334e-04
## [92,] 0.23943739 -1.976308e-04
## [93,] 0.24101272 -1.116319e-04
## [94,] 0.24108323 4.277189e-05
## [95,] 0.24224670 1.238565e-04
## [96,] 0.24238258 1.286826e-04
## [97,] 0.24440618 7.348935e-05
## [98,] 0.24534636 9.027253e-05
## [99,] 0.24543109 8.012560e-05
## [100,] 0.24602716 7.331216e-05
## [101,] 0.24824937 8.563602e-05
## [102,] 0.24860556 7.480575e-05
## [103,] 0.25051496 -9.233808e-05
## [104,] 0.25600747 -1.738584e-04
## [105,] 0.25698784 -1.837543e-04
## [106,] 0.25756298 -1.215985e-04
## [107,] 0.25996174 -7.723253e-05
## [108,] 0.26089015 -2.311284e-06
## [109,] 0.26102029 -5.464256e-05
## [110,] 0.26135688 -4.145180e-05
## [111,] 0.26197420 -6.021246e-05
## [112,] 0.26279392 -8.297598e-05
## [113,] 0.26424322 -7.271791e-05
## [114,] 0.26536118 -5.875311e-05
## [115,] 0.26614556 -1.055355e-04
## [116,] 0.26650648 -2.188283e-04
## [117,] 0.26858423 -2.524450e-04
## [118,] 0.26894438 -2.537658e-04
## [119,] 0.27075674 -2.279795e-04
## [120,] 0.27174739 -2.304471e-04
## [121,] 0.27283522 -2.855846e-04
## [122,] 0.27444322 -3.387329e-04
## [123,] 0.27507291 -1.563222e-04
## [124,] 0.27562571 -1.316054e-04
## [125,] 0.27617730 -1.958313e-05
## [126,] 0.27679246 3.873950e-05
## [127,] 0.27744283 8.526421e-05
## [128,] 0.27760892 4.939820e-05
## [129,] 0.27799266 6.289061e-05
## [130,] 0.27835671 2.968110e-05
## [131,] 0.28070853 -1.355062e-05
## [132,] 0.28123141 7.778902e-05
## [133,] 0.28138803 -5.709444e-06
## [134,] 0.28183948 1.521767e-05
## [135,] 0.28196095 3.555579e-06
## [136,] 0.28386319 -1.152022e-05
## [137,] 0.28446594 -5.219258e-05
## [138,] 0.28452431 -1.620840e-04
## [139,] 0.28730373 -2.201410e-04
## [140,] 0.28774953 -1.909496e-05
## [141,] 0.28778195 -4.930680e-06
## [142,] 0.28872323 5.075299e-05
## [143,] 0.28893446 6.304883e-05
## [144,] 0.28921269 8.450655e-06
## [145,] 0.28961345 -1.022775e-04
## [146,] 0.29093140 -1.503087e-04
## [147,] 0.29163035 1.694568e-05
## [148,] 0.29167288 1.565446e-05
## [149,] 0.29169469 -3.627734e-05
## [150,] 0.29215917 -8.890262e-05
## [151,] 0.29600330 -1.032189e-04
## [152,] 0.29674455 -1.423674e-04
## [153,] 0.29730140 -1.048808e-05
## [154,] 0.29744021 -8.302854e-06
## [155,] 0.29832650 -1.808607e-04
## [156,] 0.29952335 -1.762004e-04
## [157,] 0.29959715 -3.473698e-04
## [158,] 0.29987943 -3.428061e-04
## [159,] 0.30105946 -2.480391e-04
## [160,] 0.30280613 -2.714086e-04
## [161,] 0.30304863 -2.859202e-04
## [162,] 0.30603081 -3.068400e-04
## [163,] 0.30643001 -4.418881e-04
## [164,] 0.30932704 -4.259526e-04
## [165,] 0.31011770 -5.612857e-04
## [166,] 0.31036459 -5.784469e-04
## [167,] 0.31079487 -5.892572e-04
## [168,] 0.31179108 -5.905017e-04
## [169,] 0.31360124 -5.492938e-04
## [170,] 0.31412360 -5.631944e-04
## [171,] 0.31429273 -4.355432e-04
## [172,] 0.31444431 -3.066231e-04
## [173,] 0.31728258 -3.107952e-04
## [174,] 0.31732319 -4.653934e-04
## [175,] 0.31783631 -5.236058e-04
## [176,] 0.31871113 -5.781340e-04
## [177,] 0.31953305 -5.377470e-04
## [178,] 0.32231124 -4.788717e-04
## [179,] 0.32472166 -3.693348e-04
## [180,] 0.32584379 -3.303317e-04
## [181,] 0.32709657 -2.982085e-04
## [182,] 0.32715059 -2.969039e-04
## [183,] 0.32950585 -1.580952e-04
## [184,] 0.33020291 -1.086771e-04
## [185,] 0.33042521 2.149014e-04
## [186,] 0.33447663 4.210124e-04
## [187,] 0.33628097 5.357294e-04
## [188,] 0.33738744 4.470406e-04
## [189,] 0.33791436 7.192453e-04
## [190,] 0.33803452 7.395766e-04
## [191,] 0.33865688 8.921169e-04
## [192,] 0.33876732 1.125277e-03
## [193,] 0.33956078 1.180033e-03
## [194,] 0.34039404 1.199646e-03
## [195,] 0.34111002 8.053825e-04
## [196,] 0.34203455 5.661808e-04
## [197,] 0.34215683 5.661112e-04
## [198,] 0.34229746 1.168168e-03
## [199,] 0.34419304 1.249671e-03
## [200,] 0.34427179 1.241853e-03
## [201,] 0.34500948 1.197256e-03
## [202,] 0.34502553 1.199516e-03
## [203,] 0.34714929 1.218719e-03
## [204,] 0.35004225 1.189331e-03
## [205,] 0.35086535 1.029870e-03
## [206,] 0.35124282 1.162275e-03
## [207,] 0.35160318 1.296987e-03
## [208,] 0.35184809 1.354345e-03
## [209,] 0.35188283 1.095812e-03
## [210,] 0.35198978 8.856017e-04
## [211,] 0.35203455 9.050098e-04
## [212,] 0.35342684 1.052643e-03
## [213,] 0.35445163 1.080263e-03
## [214,] 0.35643644 1.139542e-03
## [215,] 0.35675019 1.086970e-03
## [216,] 0.35720956 1.014751e-03
## [217,] 0.35765094 8.540180e-04
## [218,] 0.35957042 1.034596e-03
## [219,] 0.36012807 1.081820e-03
## [220,] 0.36094842 1.219538e-03
## [221,] 0.36199345 1.302021e-03
## [222,] 0.36263783 1.450874e-03
## [223,] 0.36298584 1.462196e-03
## [224,] 0.36312219 1.462885e-03
## [225,] 0.36339844 1.319648e-03
## [226,] 0.36446361 1.573100e-03
## [227,] 0.36513121 1.613607e-03
## [228,] 0.36715135 1.653967e-03
## [229,] 0.36800835 1.688514e-03
## [230,] 0.36834180 1.279192e-03
## [231,] 0.36986425 1.021136e-03
## [232,] 0.36987364 9.432672e-04
## [233,] 0.36999967 9.150602e-04
## [234,] 0.37021891 9.061404e-04
## [235,] 0.37045702 1.163316e-03
## [236,] 0.37056665 1.292688e-03
## [237,] 0.37153721 1.244116e-03
## [238,] 0.37196381 1.216705e-03
## [239,] 0.37238601 1.133693e-03
## [240,] 0.37317619 8.427267e-04
## [241,] 0.37367706 7.150981e-04
## [242,] 0.37543026 7.455629e-04
## [243,] 0.37553338 1.833570e-04
## [244,] 0.37582009 1.884502e-04
## [245,] 0.37698666 2.571199e-04
## [246,] 0.37802288 3.490125e-04
## [247,] 0.37879585 4.255290e-04
## [248,] 0.37997065 8.285717e-04
## [249,] 0.38040903 1.155404e-03
## [250,] 0.38065633 1.372576e-03
## [251,] 0.38111665 1.637583e-03
## [252,] 0.38291659 1.679891e-03
## [253,] 0.38375659 1.947927e-03
## [254,] 0.38623637 1.929568e-03
## [255,] 0.38632173 1.677844e-03
## [256,] 0.38642587 1.093238e-03
## [257,] 0.38851314 1.091705e-03
## [258,] 0.38893645 1.363665e-03
## [259,] 0.39021560 1.593063e-03
## [260,] 0.39025562 1.597293e-03
## [261,] 0.39116784 1.630020e-03
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## [6] 5.982050e-07 9.918256e-07 1.272449e-06 1.302389e-06 1.357039e-06
## [11] 1.408440e-06 1.424892e-06 1.586687e-06 1.667166e-06 2.002689e-06
## [16] 2.107006e-06 2.159113e-06 2.229729e-06 2.263975e-06 2.275172e-06
## [21] 2.470246e-06 2.472418e-06 2.479000e-06 2.478144e-06 2.524822e-06
## [26] 2.617387e-06 2.754284e-06 2.763194e-06 2.877397e-06 2.898982e-06
## [31] 2.919684e-06 2.922546e-06 2.815123e-06 2.745614e-06 2.693813e-06
## [36] 2.689779e-06 2.565520e-06 2.513866e-06 2.505977e-06 2.469821e-06
## [41] 2.250348e-06 1.766024e-06 1.338754e-06 1.283713e-06 1.223653e-06
## [46] 5.903911e-07 3.026314e-08 -5.246049e-07 -9.283528e-07 -1.149905e-06
## [51] -1.392632e-06 -1.682361e-06 -1.792813e-06 -2.093269e-06 -2.621688e-06
## [56] -2.709580e-06 -2.757505e-06 -2.936272e-06 -3.076562e-06 -3.528689e-06
## [61] -3.753329e-06 -3.923921e-06 -3.961465e-06 -3.976074e-06 -4.042904e-06
## [66] -4.066267e-06 -4.363968e-06 -5.812963e-06 -5.823753e-06 -6.338801e-06
## [71] -6.544482e-06 -6.851994e-06 -6.975074e-06 -7.053271e-06 -7.125909e-06
## [76] -7.257707e-06 -7.285519e-06 -7.463432e-06 -7.440168e-06 -7.417353e-06
## [81] -7.390081e-06 -7.373853e-06 -7.274392e-06 -7.252506e-06 -7.219204e-06
## [86] -7.171884e-06 -7.149887e-06 -7.135785e-06 -7.168586e-06 -7.177984e-06
## [91] -7.179963e-06 -7.689397e-06 -7.865254e-06 -7.862238e-06 -7.718134e-06
## [96] -7.700649e-06 -7.551935e-06 -7.467064e-06 -7.460274e-06 -7.416575e-06
## [101] -7.226274e-06 -7.199629e-06 -7.375939e-06 -8.330858e-06 -8.511006e-06
## [106] -8.580942e-06 -8.766204e-06 -8.768350e-06 -8.775461e-06 -8.789413e-06
## [111] -8.826584e-06 -8.894601e-06 -8.999991e-06 -9.065675e-06 -9.148454e-06
## [116] -9.227434e-06 -9.751951e-06 -9.843344e-06 -1.025653e-05 -1.048482e-05
## [121] -1.079549e-05 -1.134017e-05 -1.143860e-05 -1.151135e-05 -1.152216e-05
## [126] -1.149833e-05 -1.144287e-05 -1.143467e-05 -1.141053e-05 -1.139973e-05
## [131] -1.143160e-05 -1.139092e-05 -1.139182e-05 -1.138495e-05 -1.138452e-05
## [136] -1.140643e-05 -1.143789e-05 -1.144735e-05 -1.205921e-05 -1.206773e-05
## [141] -1.206789e-05 -1.202011e-05 -1.200679e-05 -1.200444e-05 -1.204543e-05
## [146] -1.224353e-05 -1.223169e-05 -1.223102e-05 -1.223181e-05 -1.227311e-05
## [151] -1.266989e-05 -1.277542e-05 -1.278126e-05 -1.278242e-05 -1.294271e-05
## [156] -1.315360e-05 -1.317923e-05 -1.327600e-05 -1.356870e-05 -1.404275e-05
## [161] -1.411209e-05 -1.502714e-05 -1.520354e-05 -1.643754e-05 -1.688133e-05
## [166] -1.702414e-05 -1.727769e-05 -1.786595e-05 -1.886026e-05 -1.915445e-05
## [171] -1.922812e-05 -1.927459e-05 -2.015672e-05 -2.017562e-05 -2.044429e-05
## [176] -2.095005e-05 -2.139203e-05 -2.272243e-05 -2.361268e-05 -2.398336e-05
## [181] -2.435695e-05 -2.437299e-05 -2.474534e-05 -2.482110e-05 -2.477332e-05
## [186] -2.306763e-05 -2.210099e-05 -2.160635e-05 -2.122737e-05 -2.113849e-05
## [191] -2.058328e-05 -2.045900e-05 -1.952270e-05 -1.852308e-05 -1.794644e-05
## [196] -1.742299e-05 -1.735377e-05 -1.718949e-05 -1.482064e-05 -1.472284e-05
## [201] -1.383964e-05 -1.382039e-05 -1.123212e-05 -7.791435e-06 -6.943742e-06
## [206] -6.505023e-06 -6.037644e-06 -5.705948e-06 -5.667878e-06 -5.573163e-06
## [211] -5.532645e-06 -4.067066e-06 -2.960017e-06 -6.982460e-07 -3.572138e-07
## [216] 1.089355e-07 4.858791e-07 2.471773e-06 3.075043e-06 4.075492e-06
## [221] 5.436140e-06 6.371062e-06 6.879927e-06 7.079380e-06 7.443940e-06
## [226] 9.119561e-06 1.019679e-05 1.353804e-05 1.498511e-05 1.541165e-05
## [231] 1.696627e-05 1.697513e-05 1.709045e-05 1.728912e-05 1.756612e-05
## [236] 1.770784e-05 1.891533e-05 1.943438e-05 1.991302e-05 2.057892e-05
## [241] 2.093709e-05 2.224421e-05 2.226312e-05 2.231715e-05 2.261710e-05
## [246] 2.297875e-05 2.330768e-05 2.428108e-05 2.478759e-05 2.512703e-05
## [251] 2.588084e-05 2.890455e-05 3.054081e-05 3.532570e-05 3.546893e-05
## [256] 3.558277e-05 3.786146e-05 3.843872e-05 4.047647e-05 4.054040e-05
## [261] 4.202734e-05 4.400054e-05 4.550778e-05 4.804107e-05 4.902950e-05
## [266] 4.987498e-05 5.026324e-05 5.123372e-05 5.214436e-05 5.545937e-05
## [271] 5.782239e-05 5.926571e-05 5.960836e-05 6.029896e-05 6.222956e-05
## [276] 6.446070e-05 6.534807e-05 6.838480e-05 6.990953e-05 7.449212e-05
## [281] 7.541766e-05 7.594103e-05 7.626878e-05 7.898000e-05 7.994969e-05
## [286] 8.098387e-05 8.214611e-05 8.278977e-05 8.576777e-05 8.608111e-05
## [291] 8.710977e-05 8.879300e-05 8.935788e-05 8.999550e-05 9.087812e-05
## [296] 9.091635e-05 9.186903e-05 9.293038e-05 9.459586e-05 9.519560e-05
## [301] 9.561285e-05 9.665263e-05 9.731989e-05 9.753693e-05 9.761117e-05
## [306] 9.763400e-05 9.810879e-05 9.839107e-05 9.830445e-05 9.824888e-05
## [311] 9.792146e-05 9.791910e-05 9.799657e-05 9.823080e-05 9.858684e-05
## [316] 9.861280e-05 9.856230e-05 9.856223e-05 9.886718e-05 9.914254e-05
## [321] 9.968131e-05 1.058725e-04 1.059156e-04 1.063259e-04 1.065169e-04
## [326] 1.080578e-04 1.087676e-04 1.102718e-04 1.106456e-04 1.106427e-04
## [331] 1.102400e-04 1.101309e-04 1.092555e-04 1.090513e-04 1.091729e-04
## [336] 1.092359e-04 1.096770e-04 1.117899e-04 1.120652e-04 1.130392e-04
## [341] 1.131890e-04 1.132353e-04 1.136337e-04 1.136421e-04 1.139020e-04
## [346] 1.141350e-04 1.143405e-04 1.144224e-04 1.145714e-04 1.148663e-04
## [351] 1.148731e-04 1.166449e-04 1.177958e-04 1.178424e-04 1.179302e-04
## [356] 1.177204e-04 1.152458e-04 1.150784e-04 1.149325e-04 1.162807e-04
## [361] 1.166876e-04 1.171490e-04 1.173320e-04 1.185569e-04 1.189368e-04
## [366] 1.191614e-04 1.196162e-04 1.198493e-04 1.211378e-04 1.226964e-04
## [371] 1.231880e-04 1.257019e-04 1.270796e-04 1.282798e-04 1.292788e-04
## [376] 1.308748e-04 1.312722e-04 1.313501e-04 1.314133e-04 1.320430e-04
## [381] 1.331504e-04 1.331366e-04 1.331361e-04 1.335188e-04 1.336809e-04
## [386] 1.342599e-04 1.352332e-04 1.369290e-04 1.386468e-04 1.395805e-04
## [391] 1.477973e-04 1.487416e-04 1.494150e-04 1.512666e-04 1.552129e-04
## [396] 1.560792e-04 1.576169e-04 1.579600e-04 1.655445e-04 1.668729e-04
## [401] 1.690147e-04 1.694854e-04 1.758422e-04 1.759626e-04 1.761664e-04
## [406] 1.762209e-04 1.817849e-04 1.821804e-04 1.834617e-04 1.835447e-04
## [411] 1.873495e-04 1.886194e-04 1.892349e-04 1.896550e-04 1.931725e-04
## [416] 1.939934e-04 1.940303e-04 1.956609e-04 2.011475e-04 2.013909e-04
## [421] 2.019317e-04 2.019963e-04 2.026392e-04 2.050080e-04 2.062047e-04
## [426] 2.062345e-04 2.064048e-04 2.071690e-04 2.076694e-04 2.105554e-04
## [431] 2.107305e-04 2.109283e-04 2.110599e-04 2.110803e-04 2.118126e-04
## [436] 2.118788e-04 2.118402e-04 2.116245e-04 2.113425e-04 2.109237e-04
## [441] 2.105221e-04 2.100023e-04 2.099949e-04 2.100855e-04 2.102054e-04
## [446] 2.105417e-04 2.132661e-04 2.133428e-04 2.140349e-04 2.157590e-04
## [451] 2.162783e-04 2.180051e-04 2.228170e-04 2.233767e-04 2.421107e-04
## [456] 2.633480e-04 2.642377e-04 2.648224e-04 2.650905e-04 2.669145e-04
## [461] 2.714147e-04 2.734109e-04 2.788596e-04 2.791378e-04 2.934075e-04
## [466] 2.973297e-04 2.993303e-04 3.003745e-04 3.119597e-04 3.142360e-04
## [471] 3.194512e-04 3.208895e-04 3.250214e-04 3.366078e-04 3.417719e-04
## [476] 3.433709e-04 3.576124e-04 3.707027e-04 3.709277e-04 3.784172e-04
## [481] 3.852026e-04 3.890778e-04 4.018917e-04 4.216441e-04 4.252740e-04
## [486] 4.355172e-04 4.374389e-04 4.393077e-04 4.470391e-04 4.559091e-04
## [491] 4.560504e-04 4.570873e-04 4.657963e-04 5.035892e-04 5.055701e-04
## [496] 5.335635e-04 5.388536e-04 5.430530e-04 5.439253e-04 5.450306e-04
## [501] 5.463708e-04 5.478408e-04 5.666969e-04 5.954090e-04 6.097974e-04
## [506] 6.532561e-04 6.614450e-04 6.684607e-04 6.822337e-04 6.852159e-04
## [511] 7.036571e-04 7.434847e-04 7.636160e-04 7.821754e-04 7.996555e-04
## [516] 8.054063e-04 8.183081e-04 8.475189e-04 8.626425e-04 8.706705e-04
## [521] 8.840705e-04 8.973795e-04 9.253893e-04 9.645838e-04 9.718968e-04
## [526] 9.738290e-04 9.768567e-04 1.062926e-03 1.069557e-03 1.108398e-03
## [531] 1.130833e-03 1.175752e-03 1.215396e-03 1.217996e-03 1.242111e-03
## [536] 1.245919e-03 1.250335e-03 1.267187e-03 1.300743e-03 1.315506e-03
## [541] 1.329474e-03 1.399315e-03 1.420250e-03 1.420811e-03 1.477026e-03
## [546] 1.499759e-03 1.526808e-03 1.542092e-03 1.553369e-03 1.568851e-03
## [551] 1.581712e-03 1.596877e-03 1.675478e-03 1.723990e-03 1.727113e-03
## [556] 1.728765e-03 1.736433e-03 1.783410e-03 1.807152e-03 1.858979e-03
## [561] 1.914561e-03 1.922297e-03 1.954825e-03 1.980871e-03 2.005731e-03
## [566] 2.084938e-03 2.086535e-03 2.096796e-03 2.097248e-03 2.101801e-03
## [571] 2.104649e-03 2.116918e-03 2.123260e-03 2.178421e-03 2.239831e-03
## [576] 2.250598e-03 2.312568e-03 2.317146e-03 2.364946e-03 2.365683e-03
## [581] 2.388791e-03 2.441207e-03 2.471706e-03 2.517740e-03 2.539683e-03
## [586] 2.547753e-03 2.566312e-03 2.572506e-03 2.629522e-03 2.636561e-03
## [591] 2.650496e-03 2.666649e-03 2.706262e-03 2.731076e-03 2.749665e-03
## [596] 2.752340e-03 2.766718e-03 2.778842e-03 2.780702e-03 2.812093e-03
## [601] 2.814577e-03 2.814625e-03 2.825248e-03 2.865194e-03 2.866515e-03
## [606] 2.877263e-03 2.881732e-03 2.895788e-03 2.915903e-03 2.958498e-03
## [611] 2.987793e-03 2.997928e-03 3.053530e-03 3.101583e-03 3.148248e-03
## [616] 3.187946e-03 3.189973e-03 3.198852e-03 3.225887e-03 3.250524e-03
## [621] 3.253564e-03 3.269490e-03 3.293825e-03 3.343262e-03 3.347859e-03
## [626] 3.374908e-03 3.375517e-03 3.380525e-03 3.382803e-03 3.392380e-03
## [631] 3.438048e-03 3.467534e-03 3.533629e-03 3.586910e-03 3.666938e-03
## [636] 3.683972e-03 3.708280e-03 3.729865e-03 3.737228e-03 3.773088e-03
## [641] 3.793158e-03 3.843826e-03 3.932251e-03 3.969387e-03 3.971166e-03
## [646] 4.002670e-03 4.002993e-03 4.014222e-03 4.092484e-03 4.101273e-03
## [651] 4.116240e-03 4.172668e-03 4.209258e-03 4.226489e-03 4.253428e-03
## [656] 4.268379e-03 4.290877e-03 4.328359e-03 4.369465e-03 4.417616e-03
## [661] 4.418101e-03 4.472895e-03 4.534289e-03 4.561821e-03 4.567148e-03
## [666] 4.575872e-03 4.607558e-03 4.669803e-03 4.686069e-03 4.732613e-03
## [671] 4.782944e-03 4.786248e-03 4.805189e-03 4.827649e-03 4.884553e-03
## [676] 4.924106e-03 4.963695e-03 5.007642e-03 5.046211e-03 5.127521e-03
## [681] 5.129163e-03 5.213558e-03 5.287425e-03 5.382621e-03 5.403901e-03
## [686] 5.439120e-03 5.493896e-03 5.544642e-03 5.611753e-03 5.636168e-03
## [691] 5.661325e-03 5.758837e-03 5.782625e-03 5.865388e-03 5.985479e-03
## [696] 6.289235e-03 6.358179e-03 6.524165e-03 6.549468e-03 6.639991e-03
## [701] 6.679289e-03 6.916434e-03 7.060604e-03 7.181597e-03 7.186236e-03
## [706] 7.208354e-03 7.265974e-03 7.268533e-03 7.284917e-03 7.335641e-03
## [711] 7.421184e-03 7.430256e-03 7.469675e-03 7.531363e-03 7.540944e-03
## [716] 7.546501e-03 7.690677e-03 7.724547e-03 7.753447e-03 7.824828e-03
## [721] 7.881495e-03 7.882661e-03 7.961000e-03 7.983838e-03 8.093154e-03
## [726] 8.157447e-03 8.213895e-03 8.252704e-03 8.292952e-03 8.333929e-03
## [731] 8.343924e-03 8.360250e-03 8.373534e-03 8.421985e-03 8.435201e-03
## [736] 8.486459e-03 8.552245e-03 8.681108e-03 8.740994e-03 8.892466e-03
## [741] 8.922972e-03 9.095996e-03 9.178070e-03 9.346918e-03 9.349610e-03
## [746] 9.396858e-03 9.503894e-03 9.673569e-03 9.685474e-03 9.830782e-03
## [751] 9.856289e-03 9.951465e-03 9.970463e-03 9.970860e-03 1.007264e-02
## [756] 1.008671e-02 1.014048e-02 1.021155e-02 1.023521e-02 1.027798e-02
## [761] 1.029112e-02 1.049771e-02 1.051612e-02 1.055656e-02 1.056006e-02
## [766] 1.061518e-02 1.065869e-02 1.097816e-02 1.104801e-02 1.116791e-02
## [771] 1.139182e-02 1.144948e-02 1.149939e-02 1.169985e-02 1.173767e-02
## [776] 1.174145e-02 1.176873e-02 1.184005e-02 1.201210e-02 1.223037e-02
## [781] 1.224302e-02 1.227948e-02 1.235717e-02 1.240009e-02 1.253505e-02
## [786] 1.272076e-02 1.284645e-02 1.289429e-02 1.297650e-02 1.301828e-02
## [791] 1.306116e-02 1.336508e-02 1.337682e-02 1.357121e-02 1.359128e-02
## [796] 1.363169e-02 1.366681e-02 1.374847e-02 1.378229e-02 1.378686e-02
## [801] 1.401012e-02 1.408550e-02 1.415275e-02 1.426955e-02 1.435813e-02
## [806] 1.447339e-02 1.451451e-02 1.474491e-02 1.479782e-02 1.482380e-02
## [811] 1.496929e-02 1.537067e-02 1.557316e-02 1.579716e-02 1.583446e-02
## [816] 1.584400e-02 1.596827e-02 1.611560e-02 1.635842e-02 1.638366e-02
## [821] 1.641301e-02 1.643339e-02 1.644307e-02 1.644673e-02 1.658709e-02
## [826] 1.665921e-02 1.669630e-02 1.673115e-02 1.705415e-02 1.711655e-02
## [831] 1.722993e-02 1.723904e-02 1.724475e-02 1.751993e-02 1.763938e-02
## [836] 1.787035e-02 1.791136e-02 1.798655e-02 1.806449e-02 1.806682e-02
## [841] 1.813037e-02 1.825226e-02 1.826115e-02 1.829917e-02 1.834331e-02
## [846] 1.836402e-02 1.908761e-02 1.950887e-02 1.951579e-02 1.959331e-02
## [851] 1.972767e-02 1.981416e-02 1.989974e-02 2.000906e-02 2.021012e-02
## [856] 2.022982e-02 2.031226e-02 2.031929e-02 2.041615e-02 2.043963e-02
## [861] 2.044132e-02 2.064088e-02 2.068073e-02 2.073184e-02 2.073736e-02
## [866] 2.075222e-02 2.075428e-02 2.076226e-02 2.076868e-02 2.077378e-02
## [871] 2.079473e-02 2.081805e-02 2.081890e-02 2.081890e-02 2.081694e-02
## [876] 2.081621e-02 2.080481e-02 2.077021e-02 2.076230e-02 2.068235e-02
## [881] 2.066632e-02 2.066537e-02 2.061275e-02 2.057211e-02 2.049870e-02
## [886] 2.048782e-02 2.048138e-02 2.048174e-02 2.052214e-02 2.052920e-02
## [891] 2.058663e-02 2.058791e-02 2.060567e-02 2.064128e-02 2.065527e-02
## [896] 2.066350e-02 2.066488e-02 2.067937e-02 2.075183e-02 2.093869e-02
## [901] 2.115785e-02 2.119299e-02 2.120943e-02 2.135458e-02 2.137169e-02
## [906] 2.140017e-02 2.162020e-02 2.168968e-02 2.191825e-02 2.206210e-02
## [911] 2.215940e-02 2.227834e-02 2.228073e-02 2.228275e-02 2.229640e-02
## [916] 2.229658e-02 2.242077e-02 2.261707e-02 2.281376e-02 2.328486e-02
## [921] 2.337092e-02 2.346952e-02 2.359580e-02 2.367549e-02 2.429661e-02
## [926] 2.433143e-02 2.454004e-02 2.454517e-02 2.455391e-02 2.455506e-02
## [931] 2.463800e-02 2.465726e-02 2.468520e-02 2.473417e-02 2.481264e-02
## [936] 2.498690e-02 2.506513e-02 2.525910e-02 2.536193e-02 2.538771e-02
## [941] 2.561795e-02 2.564728e-02 2.570233e-02 2.573929e-02 2.576950e-02
## [946] 2.581249e-02 2.587874e-02 2.591765e-02 2.603081e-02 2.605475e-02
## [951] 2.607566e-02 2.615127e-02 2.621285e-02 2.624594e-02 2.628101e-02
## [956] 2.630245e-02 2.632555e-02 2.635929e-02 2.636812e-02 2.639961e-02
## [961] 2.653286e-02 2.654157e-02 2.655998e-02 2.658220e-02 2.659850e-02
## [966] 2.690553e-02 2.695782e-02 2.734616e-02 2.736412e-02 2.752511e-02
## [971] 2.754877e-02 2.764383e-02 2.781355e-02 2.783304e-02 2.790200e-02
## [976] 2.805784e-02 2.820658e-02 2.829758e-02 2.840073e-02 2.846629e-02
## [981] 2.850817e-02 2.850939e-02 2.848070e-02 2.847525e-02 2.842021e-02
## [986] 2.840947e-02 2.839386e-02 2.839291e-02 2.837215e-02 2.836668e-02
## [991] 2.837284e-02 2.840079e-02 2.859615e-02 2.871852e-02 2.879672e-02
## [996] 2.882966e-02 2.885850e-02 2.913418e-02 2.917566e-02 2.928167e-02
## [1001] 2.931551e-02 2.934791e-02 2.937936e-02 2.944128e-02 2.945098e-02
## [1006] 2.947739e-02 2.971470e-02 2.983991e-02 2.986524e-02 2.987428e-02
## [1011] 2.987940e-02 2.998062e-02 2.998090e-02 2.997943e-02 2.997007e-02
## [1016] 2.995955e-02 2.962840e-02 2.961640e-02 2.956628e-02 2.956164e-02
## [1021] 2.963830e-02 2.963840e-02 2.983540e-02 3.004340e-02 3.012862e-02
## [1026] 3.022265e-02 3.028023e-02 3.028237e-02 3.034565e-02 3.238518e-02
## [1031] 3.242400e-02 3.254227e-02 3.293515e-02 3.300160e-02 3.342062e-02
## [1036] 3.370134e-02 3.372424e-02 3.410860e-02 3.432752e-02 3.494187e-02
## [1041] 3.531027e-02 3.553685e-02 3.566269e-02 3.670992e-02 3.726495e-02
## [1046] 3.833244e-02 4.046503e-02 4.128795e-02 4.161794e-02 4.169175e-02
## [1051] 4.232224e-02 4.236996e-02 4.282884e-02 4.427075e-02 4.428137e-02
## alpha area
## 1 0.05751881 0.000000e+00
## 2 0.07104237 6.809045e-08
## 3 0.07929438 1.301971e-07
## 4 0.08378608 2.287676e-07
## 5 0.08510697 2.600994e-07
## 6 0.09448835 5.982050e-07
p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)# Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)Primero, se tiene una tabla de datos simbólica de tipo intervalo, por ejemplo abalone de RSDA. Se obtiene la matriz de centros asociada.
Sobre la matriz de centros, se aplica un modelo de regresión lineal clásico. Supongamos que se aplica un modelo de regresión lineal tomando como variable de respuesta Whole_Weight.
El modelo es: \(Y=-0.1834758-0.2693955X_{1}+1.4948113X_{2}+0.1146723X_{3}+0.6348267X_{4}+0.9660136X_{5}+0.8327747X_{6}\).
Luego, se estudia la contribución de cada variable predictora al modelo a través del diagrama de dispersión asociado.
data.c1 <- cbind(data.c[,-4],Y.c)
ggplot(data.c1, aes(x = LENGTH, y = Y.c))+geom_point()+labs(title = "LENGTH vs. Y") Lo que se está haciendo en realidad es tomar los centros de las observaciones de cada variable predictora como representantes de cada rectángulo de la agrupación rectangular formada por la variable predictora y la variable dependiente del modelo de regresión.
Gráficamente:
modelo1 <- sym.lm(WHOLE_WEIGHT ~ ., sym.data = abalone, method = "cm")
ypred1 <- sym.predict(modelo1, abalone)
ypred1$Fitted$Minimums <- round(ypred1$Fitted$Minimums, 2)
ypred1$Fitted$Maximums <- round(ypred1$Fitted$Maximums, 2)
length1 <- data.frame(lengthmin=c(0.28,0.30,0.34,0.39,0.40,0.45,0.49,0.55,0.08,0.13,0.26,0.32,0.34,0.44,0.45,0.16,0.16,0.20,0.29,0.35,0.42,0.49,0.52,0.60),lengthmax=c(0.66,0.74,0.78,0.82,0.74,0.80,0.72,0.70,0.24,0.58,0.67,0.66,0.72,0.65,0.58,0.21,0.53,0.72,0.78,0.76,0.78,0.74,0.69,0.66)) #variable LENGTH
clusters1 <- cbind(length1,ypred1$Fitted)
colnames(clusters1) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos1 <- ggplot() + geom_rect(data = clusters1,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers for the variable LENGTH",
x = "LENGTH",
y = "Y"
) +
theme_minimal()
graf1 <- rectangulos1 +
geom_point(
data = clusters1,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 2, alpha = 0.9
)
graf1 Luego, se calcula el índice de bondad de ajuste geométrico.
## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Estimating R2 Geom for variable = 2
## Estimating R2 Geom for variable = 3
## Estimating R2 Geom for variable = 4
## Estimating R2 Geom for variable = 5
## Estimating R2 Geom for variable = 6
Ahora, además de la matriz de centros se crea la matriz de rangos y se estudian los centros más rangos y los centros menos rangos.
data.r <- interval.ranges(data)
data.r <- round(data.r,2)
data.cmasr <- data.c + data.r
data.cmenosr <- data.c - data.rSe crea un modelo de regresión lineal clásico con los centros más rangos.
El modelo es \(Y=-0.19494+0.77978X_{1}-0.05459X_{2}+0.06312X_{3}+0.63785X_{4}+1.28787X_{5}+0.89348X_{6}\)
Luego, se estudia la contribución de cada variable predictora al modelo a través del diagrama de dispersión asociado.
data.cmasr1 <- cbind(data.cmasr[,-4],Y.cmasr)
ggplot(data.cmasr1, aes(x = LENGTH, y = Y.cmasr))+geom_point()+labs(title = "LENGTH vs. Y") #Nube de puntos LENGTH vs Y.cmasrmodelo2 <- sym.lm(WHOLE_WEIGHT ~ ., sym.data = abalone, method = "crm")
ypred2 <- sym.predict(modelo2, abalone)
ypred2$Fitted$Minimums <- round(ypred2$Fitted$Minimums, 2)
ypred2$Fitted$Maximums <- round(ypred2$Fitted$Maximums, 2)
clusters2 <- cbind(length1,ypred2$Fitted)
colnames(clusters2) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos2 <- ggplot() + geom_rect(data = clusters2,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers plus ranges for the variable LENGTH", x="LENGTH",
y = "Y"
) +
theme_minimal()
graf2 <- rectangulos2 +
geom_point(
data = clusters2,
aes(x = lengthmax, y = ymax),
color = "red", size = 3, alpha = 0.9
)
graf2## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Estimating R2 Geom for variable = 2
## Estimating R2 Geom for variable = 3
## Estimating R2 Geom for variable = 4
## Estimating R2 Geom for variable = 5
## Estimating R2 Geom for variable = 6
##
## Call:
## spatgeom_xy(x = x, y = y, scale = scale, nalphas = nalphas, envelope = envelope, mc_cores = mc_cores)
##
## Number of variables: 6
##
## Number of observations: 24
## # A tibble: 6 × 5
## variable_name mean_n intensity alpha geom_corr
## <chr> <dbl> <dbl> <fct> <fct>
## 1 DIAMETER 24 16.4 (0.034,0.697] (0.91,0.999]
## 2 HEIGHT 24 7.74 (0.0257,0.637] (0.777,1]
## 3 LENGTH 24 13.9 (0.0306,0.748] (0.912,1]
## 4 SHELL_WEIGHT 24 8.45 (0.0521,0.603] (0.879,1]
## 5 SHUCKED_WEIGHT 24 5.65 (0.0507,0.791] (0.909,1]
## 6 VISCERA_WEIGHT 24 11.1 (0.0404,0.444] (0.937,0.999]
Se repite lo anterior, pero ahora usando centros menos rangos.
El modelo es \(Y=-0.01563+1.11565X_{1}-1.39136X_{2}-0.05412X_{3}+0.30067X_{4}+1.70071X_{5}+1.77761X_{6}\)
data.cmenosr1 <- cbind(data.cmenosr[,-4],Y.cmenosr)
ggplot(data.cmenosr1, aes(x = LENGTH, y = Y.cmenosr))+geom_point()+labs(title = "LENGTH vs. Y") #Nube de puntos LENGTH vs Y.cmasrmodelo3 <- sym.lm(WHOLE_WEIGHT ~ ., sym.data = abalone, method = "crm")
ypred3 <- sym.predict(modelo3, abalone)
ypred3$Fitted$Minimums <- round(ypred3$Fitted$Minimums,2)
ypred3$Fitted$Maximums <- round(ypred3$Fitted$Maximums,2)
clusters3 <- cbind(length1,ypred3$Fitted)
colnames(clusters3) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos3 <- ggplot() + geom_rect(data = clusters3,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers minus ranges for the variable LENGTH",
x = "LENGTH",
y = "Y"
) +
theme_minimal()
graf3 <- rectangulos3 +
geom_point(data = clusters3,
aes(x = lengthmin, y = ymin),
color = "green", size = 3, alpha = 0.9
)
graf3## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Estimating R2 Geom for variable = 2
## Estimating R2 Geom for variable = 3
## Estimating R2 Geom for variable = 4
## Estimating R2 Geom for variable = 5
## Estimating R2 Geom for variable = 6
geom_indicesc <- indice1$results[[1]]$geom_indices #centros
geom_indicescmasr <- indice2$results[[1]]$geom_indices #centrosmasrangos
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el mínimo valor asociado en geom_corr
ggplot(geom_indicescmasr1, aes(x=alpha,y=geom_corr))+geom_point()geom_indicescmenosr <- indice3$results[[1]]$geom_indices #centrosmenosrangos
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el máximo valor asociado en geom_corr
ggplot(geom_indicescmenosr1, aes(x=alpha,y=geom_corr))+geom_point()# Etiquetas para identificar cada curva
geom_indicesc$label <- "centros"
geom_indicescmasr$label <- "centros más rangos"
geom_indicescmenosr$label <- "centros menos rangos"
# Combinar los datos
data_combined <- rbind(geom_indicesc,geom_indicescmasr, geom_indicescmenosr )
data_combined1 <- rbind(geom_indicescmasr1, geom_indicescmenosr1)
data_combined1 <- rbind(c(0,1),data_combined1)
# Crear el gráfico
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica para la variable Syst",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))#Área acumulada entre las curvas: centros menos rangos y centros más rangos.
library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmasr1$alpha, geom_indicescmenosr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
ggplot(table.cmasr, aes(x=alpha.vals, geom_corr.cmasr))+geom_point()table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
ggplot(table.cmenosr, aes(x=alpha.vals, geom_corr.cmenosr))+geom_point()## alpha.vals diff.geom_corr
## [1,] 0.01802776 0.0001120065
## [2,] 0.02236068 0.0007425235
## [3,] 0.02500000 0.0013730405
## [4,] 0.02692582 0.0013730405
## [5,] 0.02915476 0.0015306698
## [6,] 0.03162278 0.0016882990
## [7,] 0.03201562 0.0032645916
## [8,] 0.03201562 0.0032645916
## [9,] 0.03605551 0.0032808190
## [10,] 0.03640055 0.0034263714
## [11,] 0.03640055 0.0034263714
## [12,] 0.03905125 0.0040429249
## [13,] 0.04031129 0.0041564510
## [14,] 0.04031129 0.0041564510
## [15,] 0.04242641 0.0044860689
## [16,] 0.04716991 0.0057410552
## [17,] 0.04716991 0.0057410552
## [18,] 0.05000000 0.0047602901
## [19,] 0.06082763 0.0046183024
## [20,] 0.06403124 0.0027475600
## [21,] 0.06670832 0.0026580754
## [22,] 0.06946222 0.0070060729
## [23,] 0.07071068 0.0084096964
## [24,] 0.07158911 0.0083440835
## [25,] 0.07566373 0.0061061826
## [26,] 0.08000000 0.0031299895
## [27,] 0.08062258 0.0029436300
## [28,] 0.08544004 0.0036289790
## [29,] 0.09013878 0.0055382609
## [30,] 0.09013878 0.0055382609
## [31,] 0.09513149 0.0103554269
## [32,] 0.09552487 0.0104410471
## [33,] 0.09617692 0.0102122080
## [34,] 0.10000000 0.0111074824
## [35,] 0.10049876 0.0119487758
## [36,] 0.10124228 0.0134264555
## [37,] 0.10511898 0.0142874529
## [38,] 0.10793517 0.0143745133
## [39,] 0.11401754 0.0147249365
## [40,] 0.12539936 0.0170354227
## [41,] 0.12658989 0.0172764877
## [42,] 0.13536986 0.0195194870
## [43,] 0.13793114 0.0199042255
## [44,] 0.15074813 0.0186910880
## [45,] 0.16710775 0.0211025111
## [46,] 0.17066048 0.0221339335
## [47,] 0.17356555 0.0204585161
## [48,] 0.17464249 0.0200146978
## [49,] 0.17951323 0.0200584340
## [50,] 0.20099751 0.0269589484
## [51,] 0.22000000 0.0296404952
## [52,] 0.23505319 0.0335233383
## [53,] 0.23584953 0.0334318534
## [54,] 0.24135037 0.0373769500
## [55,] 0.24748737 0.0562651702
## [56,] 0.24839485 0.0594062508
## [57,] 0.29920729 0.0774123036
## [58,] 0.30008332 0.0777430629
## [59,] 0.31780497 0.0787324858
## [60,] 0.35510562 0.1191705005
## [61,] 0.36280160 0.1262083805
## [62,] 0.37406550 0.1280914689
## [63,] 0.47447339 0.1649297176
## [64,] 0.48703183 0.1673596859
## [65,] 0.58860003 0.1923946039
## [66,] 0.65370100 0.2076077809
## [67,] 1.06894808 0.1436509645
## [68,] 1.36792726 0.1272456219
## [69,] 1.46400990 0.1202479448
## [1] 0.000000e+00 3.217297e-06 6.841191e-06 9.485426e-06 1.289719e-05
## [6] 1.706394e-05 1.834642e-05 1.834642e-05 3.160057e-05 3.278279e-05
## [11] 3.278279e-05 4.349937e-05 4.873667e-05 4.873667e-05 5.822523e-05
## [16] 8.545792e-05 8.545792e-05 9.892999e-05 1.489352e-04 1.577374e-04
## [21] 1.648532e-04 1.841473e-04 1.946464e-04 2.019761e-04 2.268565e-04
## [26] 2.404290e-04 2.422616e-04 2.597441e-04 2.857669e-04 2.857669e-04
## [31] 3.374685e-04 3.415758e-04 3.482347e-04 3.906995e-04 3.966591e-04
## [36] 4.066420e-04 4.620301e-04 5.025114e-04 5.920740e-04 7.859681e-04
## [41] 8.065363e-04 9.779169e-04 1.028897e-03 1.268461e-03 1.613690e-03
## [46] 1.692326e-03 1.751759e-03 1.773314e-03 1.871013e-03 2.450207e-03
## [51] 3.013450e-03 3.518083e-03 3.544706e-03 3.750311e-03 4.095610e-03
## [56] 4.149520e-03 8.083028e-03 8.151134e-03 9.546403e-03 1.399154e-02
## [61] 1.496284e-02 1.640565e-02 3.296589e-02 3.506767e-02 5.460884e-02
## [66] 6.812431e-02 1.277750e-01 1.658187e-01 1.773725e-01
## alpha area
## 1 0.01802776 0.000000e+00
## 2 0.02236068 3.217297e-06
## 3 0.02500000 6.841191e-06
## 4 0.02692582 9.485426e-06
## 5 0.02915476 1.289719e-05
## 6 0.03162278 1.706394e-05
## 7 0.03201562 1.834642e-05
## 8 0.03201562 1.834642e-05
## 9 0.03605551 3.160057e-05
## 10 0.03640055 3.278279e-05
## 11 0.03640055 3.278279e-05
## 12 0.03905125 4.349937e-05
## 13 0.04031129 4.873667e-05
## 14 0.04031129 4.873667e-05
## 15 0.04242641 5.822523e-05
## 16 0.04716991 8.545792e-05
## 17 0.04716991 8.545792e-05
## 18 0.05000000 9.892999e-05
## 19 0.06082763 1.489352e-04
## 20 0.06403124 1.577374e-04
## 21 0.06670832 1.648532e-04
## 22 0.06946222 1.841473e-04
## 23 0.07071068 1.946464e-04
## 24 0.07158911 2.019761e-04
## 25 0.07566373 2.268565e-04
## 26 0.08000000 2.404290e-04
## 27 0.08062258 2.422616e-04
## 28 0.08544004 2.597441e-04
## 29 0.09013878 2.857669e-04
## 30 0.09013878 2.857669e-04
## 31 0.09513149 3.374685e-04
## 32 0.09552487 3.415758e-04
## 33 0.09617692 3.482347e-04
## 34 0.10000000 3.906995e-04
## 35 0.10049876 3.966591e-04
## 36 0.10124228 4.066420e-04
## 37 0.10511898 4.620301e-04
## 38 0.10793517 5.025114e-04
## 39 0.11401754 5.920740e-04
## 40 0.12539936 7.859681e-04
## 41 0.12658989 8.065363e-04
## 42 0.13536986 9.779169e-04
## 43 0.13793114 1.028897e-03
## 44 0.15074813 1.268461e-03
## 45 0.16710775 1.613690e-03
## 46 0.17066048 1.692326e-03
## 47 0.17356555 1.751759e-03
## 48 0.17464249 1.773314e-03
## 49 0.17951323 1.871013e-03
## 50 0.20099751 2.450207e-03
## 51 0.22000000 3.013450e-03
## 52 0.23505319 3.518083e-03
## 53 0.23584953 3.544706e-03
## 54 0.24135037 3.750311e-03
## 55 0.24748737 4.095610e-03
## 56 0.24839485 4.149520e-03
## 57 0.29920729 8.083028e-03
## 58 0.30008332 8.151134e-03
## 59 0.31780497 9.546403e-03
## 60 0.35510562 1.399154e-02
## 61 0.36280160 1.496284e-02
## 62 0.37406550 1.640565e-02
## 63 0.47447339 3.296589e-02
## 64 0.48703183 3.506767e-02
## 65 0.58860003 5.460884e-02
## 66 0.65370100 6.812431e-02
## 67 1.06894808 1.277750e-01
## 68 1.36792726 1.658187e-01
## 69 1.46400990 1.773725e-01
p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)#Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)data.c1 <- cbind(data.c[,-4],Y.c)
ggplot(data.c1, aes(x = DIAMETER, y = Y.c))+geom_point()+labs(title = "LENGTH vs. Y") Lo que se está haciendo en realidad es tomar los centros de las observaciones de cada variable predictora como representantes de cada rectángulo de la agrupación rectangular formada por la variable predictora y la variable dependiente del modelo de regresión.
Gráficamente:
diameter1 <- data.frame(lengthmin=c(0.20,0.22,0.26,0.30,0.32,0.38,0.36,0.46,0.06,0.10,0.20,0.24,0.26,0.33,0.36,0.11,0.12,0.16,0.22,0.26,0.32,0.38,0.40,0.50),lengthmax=c(0.48,0.58,0.63,0.65,0.60,0.63,0.58,0.58,0.18,0.45,0.50,0.52,0.55,0.52,0.44,0.15,0.41,0.57,0.63,0.60,0.59,0.59,0.54,0.54)) #variable DIAMETER
clusters1.1 <- cbind(diameter1,ypred1$Fitted)
colnames(clusters1.1) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos1.1 <- ggplot() + geom_rect(data = clusters1.1,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.2, color = "black"
) +
labs(
title = "Centers for the variable DIAMETER",
x = "DIAMETER",
y = "Y"
) +
theme_minimal()
graf1.1 <- rectangulos1.1 +
geom_point(
data = clusters1.1,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 2, alpha = 0.9
)
graf1.1data.cmasr1 <- cbind(data.cmasr[,-4],Y.cmasr)
ggplot(data.cmasr1, aes(x = DIAMETER, y = Y.cmasr))+geom_point()+labs(title = "DIAMETER vs. Y") clusters2.1 <- cbind(diameter1,ypred2$Fitted)
colnames(clusters2.1) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos2.1 <- ggplot() + geom_rect(data = clusters2.1,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers plus ranges for the variable DIAMETER", x="DIAMETER",
y = "Y"
) +
theme_minimal()
graf2.1 <- rectangulos2.1 +
geom_point(
data = clusters2.1,
aes(x = lengthmax, y = ymax),
color = "red", size = 3, alpha = 0.9
)
graf2.1data.cmenosr1 <- cbind(data.cmenosr[,-4],Y.cmenosr)
ggplot(data.cmenosr1, aes(x = DIAMETER, y = Y.cmenosr))+geom_point()+labs(title = "DIAMETER vs. Y") clusters3.1 <- cbind(diameter1,ypred3$Fitted)
colnames(clusters3.1) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos3.1 <- ggplot() + geom_rect(data = clusters3.1,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Point clouds of centers and extremes",
x = "Variable 1",
y = "Y"
) +
theme_minimal()
graf3.1 <- rectangulos3.1 +
geom_point(data = clusters3.1,
aes(x = lengthmin, y = ymin),
color = "green", size = 2, alpha = 0.9
)+ geom_point(
data = clusters2.1,
aes(x = lengthmax, y = ymax),
color = "red", size = 2, alpha = 0.9
)+
geom_point(
data = clusters1.1,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 2, alpha = 0.9
)
graf3.1geom_indicesc <- indice1$results[[2]]$geom_indices #centros
geom_indicescmasr <- indice2$results[[2]]$geom_indices #centrosmasrangos
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el mínimo valor asociado en geom_corr
ggplot(geom_indicescmasr1, aes(x=alpha,y=geom_corr))+geom_point()geom_indicescmenosr <- indice3$results[[2]]$geom_indices #centrosmenosrangos
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el máximo valor asociado en geom_corr
ggplot(geom_indicescmenosr1, aes(x=alpha,y=geom_corr))+geom_point()# Etiquetas para identificar cada curva
geom_indicesc$label <- "centros"
geom_indicescmasr$label <- "centros más rangos"
geom_indicescmenosr$label <- "centros menos rangos"
# Combinar los datos
data_combined <- rbind(geom_indicesc,geom_indicescmasr, geom_indicescmenosr )
data_combined1 <- rbind(geom_indicescmasr1, geom_indicescmenosr1)
# Crear el gráfico
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica para la variable DIAMETER",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmasr1$alpha, geom_indicescmenosr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
ggplot(table.cmasr, aes(x=alpha.vals, geom_corr.cmasr))+geom_point()table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
ggplot(table.cmenosr, aes(x=alpha.vals, geom_corr.cmenosr))+geom_point()## alpha.vals diff.geom_corr
## [1,] 0.01414214 -5.010507e-04
## [2,] 0.02061553 -4.567734e-05
## [3,] 0.02236068 -4.567734e-05
## [4,] 0.02236068 1.411518e-03
## [5,] 0.02500000 1.957966e-03
## [6,] 0.02500000 3.141937e-03
## [7,] 0.03162278 3.506235e-03
## [8,] 0.03162278 3.870534e-03
## [9,] 0.03162278 3.870534e-03
## [10,] 0.03354102 5.236654e-03
## [11,] 0.03535534 5.893799e-03
## [12,] 0.03605551 6.137749e-03
## [13,] 0.03605551 6.502047e-03
## [14,] 0.04031129 6.625529e-03
## [15,] 0.04031129 6.625529e-03
## [16,] 0.04123106 5.972963e-03
## [17,] 0.04472136 6.908696e-03
## [18,] 0.05000000 6.864848e-03
## [19,] 0.05315073 6.191568e-03
## [20,] 0.06020797 5.830334e-03
## [21,] 0.06184658 5.160336e-03
## [22,] 0.06324555 5.031947e-03
## [23,] 0.06403124 7.339810e-03
## [24,] 0.06576473 7.989346e-03
## [25,] 0.07071068 6.842667e-03
## [26,] 0.07648529 5.925128e-03
## [27,] 0.08000000 5.716900e-03
## [28,] 0.08062258 5.481027e-03
## [29,] 0.08246211 4.802202e-03
## [30,] 0.08845903 3.382224e-03
## [31,] 0.08860023 7.694121e-03
## [32,] 0.09013878 7.944798e-03
## [33,] 0.09055385 7.368050e-03
## [34,] 0.09219544 8.056195e-03
## [35,] 0.09513149 8.818497e-03
## [36,] 0.09617692 9.029980e-03
## [37,] 0.09708244 7.937025e-03
## [38,] 0.09823441 8.433267e-03
## [39,] 0.10688779 9.048712e-03
## [40,] 0.10770330 7.136662e-03
## [41,] 0.11011358 6.400595e-03
## [42,] 0.11101802 6.303947e-03
## [43,] 0.12257651 9.113461e-03
## [44,] 0.12539936 8.407843e-03
## [45,] 0.12747549 8.599094e-03
## [46,] 0.13583078 8.581774e-03
## [47,] 0.14849242 1.020693e-02
## [48,] 0.15000000 1.041223e-02
## [49,] 0.17029386 1.228544e-02
## [50,] 0.17117243 1.034592e-02
## [51,] 0.17182840 8.070621e-03
## [52,] 0.20000000 1.324926e-02
## [53,] 0.22022716 1.688006e-02
## [54,] 0.23021729 1.902845e-02
## [55,] 0.23632605 4.224508e-02
## [56,] 0.23690715 4.435955e-02
## [57,] 0.24253866 5.200286e-02
## [58,] 0.24682990 5.182597e-02
## [59,] 0.26800187 5.372343e-02
## [60,] 0.27771388 4.965851e-02
## [61,] 0.29652150 5.272071e-02
## [62,] 0.29920729 5.267673e-02
## [63,] 0.31184932 5.238803e-02
## [64,] 0.31894357 5.227292e-02
## [65,] 0.34179672 7.759101e-02
## [66,] 0.35106979 8.887216e-02
## [67,] 0.46671726 1.219334e-01
## [68,] 0.64352545 1.702145e-01
## [69,] 0.69146583 1.654053e-01
## [70,] 0.72292807 1.623309e-01
## [71,] 1.06303810 1.217147e-01
## [72,] 1.35875862 8.594917e-02
## [1] 0.000000e+00 -2.956874e-07 -3.754012e-07 -3.754012e-07 4.792297e-06
## [6] 4.792297e-06 2.801331e-05 2.801331e-05 2.801331e-05 3.805849e-05
## [11] 4.875172e-05 5.304921e-05 5.304921e-05 8.124598e-05 8.124598e-05
## [16] 8.673971e-05 1.108532e-04 1.470902e-04 1.665982e-04 2.077443e-04
## [21] 2.162000e-04 2.232396e-04 2.290064e-04 2.428558e-04 2.766993e-04
## [26] 3.109146e-04 3.310079e-04 3.344202e-04 3.432541e-04 3.635370e-04
## [31] 3.646233e-04 3.768469e-04 3.799051e-04 3.931301e-04 4.190216e-04
## [36] 4.284618e-04 4.356490e-04 4.453639e-04 5.236658e-04 5.294858e-04
## [41] 5.449130e-04 5.506146e-04 6.559524e-04 6.796865e-04 6.975393e-04
## [46] 7.692425e-04 8.984790e-04 9.141762e-04 1.163495e-03 1.172585e-03
## [51] 1.177879e-03 1.551132e-03 1.892567e-03 2.082664e-03 2.340729e-03
## [56] 2.366507e-03 2.659361e-03 2.881759e-03 4.019189e-03 4.501474e-03
## [61] 5.493025e-03 5.634503e-03 6.296794e-03 6.667631e-03 8.440831e-03
## [66] 9.264949e-03 2.336624e-02 5.346155e-02 6.139115e-02 6.649844e-02
## [71] 1.078948e-01 1.333118e-01
## alpha area
## 1 0.01414214 0.000000e+00
## 2 0.02061553 -2.956874e-07
## 3 0.02236068 -3.754012e-07
## 4 0.02236068 -3.754012e-07
## 5 0.02500000 4.792297e-06
## 6 0.02500000 4.792297e-06
## 7 0.03162278 2.801331e-05
## 8 0.03162278 2.801331e-05
## 9 0.03162278 2.801331e-05
## 10 0.03354102 3.805849e-05
## 11 0.03535534 4.875172e-05
## 12 0.03605551 5.304921e-05
## 13 0.03605551 5.304921e-05
## 14 0.04031129 8.124598e-05
## 15 0.04031129 8.124598e-05
## 16 0.04123106 8.673971e-05
## 17 0.04472136 1.108532e-04
## 18 0.05000000 1.470902e-04
## 19 0.05315073 1.665982e-04
## 20 0.06020797 2.077443e-04
## 21 0.06184658 2.162000e-04
## 22 0.06324555 2.232396e-04
## 23 0.06403124 2.290064e-04
## 24 0.06576473 2.428558e-04
## 25 0.07071068 2.766993e-04
## 26 0.07648529 3.109146e-04
## 27 0.08000000 3.310079e-04
## 28 0.08062258 3.344202e-04
## 29 0.08246211 3.432541e-04
## 30 0.08845903 3.635370e-04
## 31 0.08860023 3.646233e-04
## 32 0.09013878 3.768469e-04
## 33 0.09055385 3.799051e-04
## 34 0.09219544 3.931301e-04
## 35 0.09513149 4.190216e-04
## 36 0.09617692 4.284618e-04
## 37 0.09708244 4.356490e-04
## 38 0.09823441 4.453639e-04
## 39 0.10688779 5.236658e-04
## 40 0.10770330 5.294858e-04
## 41 0.11011358 5.449130e-04
## 42 0.11101802 5.506146e-04
## 43 0.12257651 6.559524e-04
## 44 0.12539936 6.796865e-04
## 45 0.12747549 6.975393e-04
## 46 0.13583078 7.692425e-04
## 47 0.14849242 8.984790e-04
## 48 0.15000000 9.141762e-04
## 49 0.17029386 1.163495e-03
## 50 0.17117243 1.172585e-03
## 51 0.17182840 1.177879e-03
## 52 0.20000000 1.551132e-03
## 53 0.22022716 1.892567e-03
## 54 0.23021729 2.082664e-03
## 55 0.23632605 2.340729e-03
## 56 0.23690715 2.366507e-03
## 57 0.24253866 2.659361e-03
## 58 0.24682990 2.881759e-03
## 59 0.26800187 4.019189e-03
## 60 0.27771388 4.501474e-03
## 61 0.29652150 5.493025e-03
## 62 0.29920729 5.634503e-03
## 63 0.31184932 6.296794e-03
## 64 0.31894357 6.667631e-03
## 65 0.34179672 8.440831e-03
## 66 0.35106979 9.264949e-03
## 67 0.46671726 2.336624e-02
## 68 0.64352545 5.346155e-02
## 69 0.69146583 6.139115e-02
## 70 0.72292807 6.649844e-02
## 71 1.06303810 1.078948e-01
## 72 1.35875862 1.333118e-01
p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)#Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)data.c1 <- cbind(data.c[,-4],Y.c)
ggplot(data.c1, aes(x = HEIGHT, y = Y.c))+geom_point()+labs(title = "HEIGHT vs. Y") Lo que se está haciendo en realidad es tomar los centros de las observaciones de cada variable predictora como representantes de cada rectángulo de la agrupación rectangular formada por la variable predictora y la variable dependiente del modelo de regresión.
Gráficamente:
height1 <- data.frame(lengthmin=c(0.07,0.02,0.06,0.10,0.10,0.14,0.12,0.18,0.01,0.00,0.00,0.08,0.08,0.12,0.12,0.04,0.02,0.04,0.06,0.08,0.12,0.13,0.14,0.20),lengthmax=c(0.18,1.13,0.23,0.25,0.24,0.22,0.21,0.22,0.06,0.15,0.18,0.19,0.22,0.20,0.18,0.05,0.16,0.20,0.52,0.24,0.24,0.23,0.22,0.22)) #variable HEIGHT
clusters1.2 <- cbind(height1,ypred1$Fitted)
colnames(clusters1.2) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos1.2 <- ggplot() + geom_rect(data = clusters1.2,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.2, color = "black"
) +
labs(
title = "Centers for the variable HEIGHT",
x = "HEIGHT",
y = "Y"
) +
theme_minimal()
graf1.2 <- rectangulos1.2 +
geom_point(
data = clusters1.2,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 2, alpha = 0.9
)
graf1.2 data.cmasr1 <- cbind(data.cmasr[,-4],Y.cmasr)
ggplot(data.cmasr1, aes(x = HEIGHT, y = Y.cmasr))+geom_point()+labs(title = "HEIGHT vs. Y") clusters2.2 <- cbind(height1,ypred2$Fitted)
colnames(clusters2.2) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos2.2 <- ggplot() + geom_rect(data = clusters2.2,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers plus ranges for the variable HEIGHT", x="HEIGHT",
y = "Y"
) +
theme_minimal()
graf2.2 <- rectangulos2.2 +
geom_point(
data = clusters2.2,
aes(x = lengthmax, y = ymax),
color = "red", size = 3, alpha = 0.9
)
graf2.2data.cmenosr1 <- cbind(data.cmenosr[,-4],Y.cmenosr)
ggplot(data.cmenosr1, aes(x = HEIGHT, y = Y.cmenosr))+geom_point()+labs(title = "DIAMETER vs. Y") clusters3.2 <- cbind(height1,ypred3$Fitted)
colnames(clusters3.2) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos3.2 <- ggplot() + geom_rect(data = clusters3.2,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers minus ranges for the variable HEIGHT",
x = "HEIGHT",
y = "Y"
) +
theme_minimal()
graf3.2 <- rectangulos3.2 +
geom_point(data = clusters3.2,
aes(x = lengthmin, y = ymin),
color = "green", size = 3, alpha = 0.9
)
graf3.2geom_indicesc <- indice1$results[[3]]$geom_indices #centros
geom_indicescmasr <- indice2$results[[3]]$geom_indices #centrosmasrangos
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el mínimo valor asociado en geom_corr
ggplot(geom_indicescmasr1, aes(x=alpha,y=geom_corr))+geom_point()geom_indicescmenosr <- indice3$results[[3]]$geom_indices #centrosmenosrangos
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el máximo valor asociado en geom_corr
ggplot(geom_indicescmenosr1, aes(x=alpha,y=geom_corr))+geom_point()# Etiquetas para identificar cada curva
geom_indicesc$label <- "centros"
geom_indicescmasr$label <- "centros más rangos"
geom_indicescmenosr$label <- "centros menos rangos"
# Combinar los datos
data_combined <- rbind(geom_indicesc,geom_indicescmasr, geom_indicescmenosr )
data_combined1 <- rbind(geom_indicescmasr1, geom_indicescmenosr1)
# Crear el gráfico
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica para la variable HEIGHT",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmasr1$alpha, geom_indicescmenosr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
ggplot(table.cmasr, aes(x=alpha.vals, geom_corr.cmasr))+geom_point()table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
ggplot(table.cmenosr, aes(x=alpha.vals, geom_corr.cmenosr))+geom_point()## alpha.vals diff.geom_corr
## [1,] 0.01414214 0.0007228854
## [2,] 0.01500000 0.0019523936
## [3,] 0.02000000 0.0019523936
## [4,] 0.02061553 0.0027720658
## [5,] 0.02061553 0.0035917379
## [6,] 0.02236068 0.0048212461
## [7,] 0.02500000 0.0056409182
## [8,] 0.02692582 0.0073093740
## [9,] 0.03162278 0.0113322618
## [10,] 0.03162278 0.0129716061
## [11,] 0.03162278 0.0129716061
## [12,] 0.03500000 0.0186759760
## [13,] 0.03535534 0.0203118129
## [14,] 0.03640055 0.0280883814
## [15,] 0.03807887 0.0372931270
## [16,] 0.04000000 0.0382732793
## [17,] 0.04031129 0.0383061208
## [18,] 0.04123106 0.0387814770
## [19,] 0.04609772 0.0451181535
## [20,] 0.06020797 0.0475314107
## [21,] 0.06020797 0.0475314107
## [22,] 0.06324555 0.0501857712
## [23,] 0.06576473 0.0524705353
## [24,] 0.07071068 0.0527812704
## [25,] 0.07566373 0.0529299117
## [26,] 0.07648529 0.0529920638
## [27,] 0.08062258 0.0561948328
## [28,] 0.08631338 0.0607669036
## [29,] 0.09055385 0.0617632425
## [30,] 0.09552487 0.0626457139
## [31,] 0.10111874 0.0648797609
## [32,] 0.10198039 0.0649591454
## [33,] 0.10511898 0.0651813762
## [34,] 0.10606602 0.0655987524
## [35,] 0.11011358 0.0662024758
## [36,] 0.11543396 0.0670859265
## [37,] 0.12093387 0.0674891073
## [38,] 0.12539936 0.0676579870
## [39,] 0.12589678 0.0700949015
## [40,] 0.12816006 0.0865926981
## [41,] 0.13509256 0.0874349083
## [42,] 0.15033296 0.0897377629
## [43,] 0.17334936 0.0932501557
## [44,] 0.17507141 0.0913904413
## [45,] 0.18027756 0.0915444775
## [46,] 0.18560711 0.0917189880
## [47,] 0.19448650 0.0895788887
## [48,] 0.20886599 0.0901580500
## [49,] 0.21708293 0.0905918177
## [50,] 0.23584953 0.1208457877
## [51,] 0.25223997 0.1503439841
## [52,] 0.26076810 0.1521643056
## [53,] 0.31184932 0.1672753412
## [54,] 0.33000000 0.1745228845
## [55,] 0.34234486 0.1795039584
## [56,] 0.45024993 0.2163580680
## [57,] 0.45400991 0.1464426057
## [58,] 0.46010868 0.1191031189
## [59,] 0.46270941 0.0942506732
## [60,] 0.47055818 0.0887193863
## [61,] 0.50982840 0.0708803823
## [62,] 0.53956001 0.0642094976
## [63,] 0.54664888 0.0655506576
## [64,] 0.56678920 0.0656735804
## [65,] 0.57212324 0.0659928611
## [66,] 0.59076222 0.0636600651
## [67,] 0.61459336 0.0380438565
## [68,] 0.63780875 0.0301073486
## [69,] 0.76134749 -0.0254482070
## [70,] 0.82602966 -0.0411437806
## [71,] 1.21652168 -0.1599333018
## [72,] 1.24788822 -0.1631272623
## [1] 0.000000e+00 1.674889e-06 1.143686e-05 1.314314e-05 1.314314e-05
## [6] 2.155695e-05 3.644514e-05 5.052171e-05 1.037488e-04 1.037488e-04
## [11] 1.037488e-04 1.668217e-04 1.740393e-04 2.033976e-04 2.659872e-04
## [16] 3.395154e-04 3.514396e-04 3.871096e-04 6.066846e-04 1.277365e-03
## [21] 1.277365e-03 1.429808e-03 1.561991e-03 1.823044e-03 2.085209e-03
## [26] 2.128745e-03 2.361239e-03 2.707051e-03 2.968957e-03 3.280369e-03
## [31] 3.643299e-03 3.699271e-03 3.903848e-03 3.965973e-03 4.233931e-03
## [36] 4.590854e-03 4.962038e-03 5.264164e-03 5.299031e-03 5.495014e-03
## [41] 6.101157e-03 7.468796e-03 9.615079e-03 9.772458e-03 1.024905e-02
## [46] 1.073787e-02 1.153328e-02 1.282971e-02 1.357409e-02 1.584196e-02
## [51] 1.830616e-02 1.960384e-02 2.814847e-02 3.131618e-02 3.353213e-02
## [56] 5.687826e-02 5.742888e-02 5.815526e-02 5.840038e-02 5.909672e-02
## [61] 6.188021e-02 6.378926e-02 6.425394e-02 6.557663e-02 6.592864e-02
## [66] 6.711520e-02 6.802183e-02 6.872078e-02 6.557694e-02 6.291567e-02
## [71] 4.629927e-04 -4.653744e-03
## alpha area
## 1 0.01414214 0.000000e+00
## 2 0.01500000 1.674889e-06
## 3 0.02000000 1.143686e-05
## 4 0.02061553 1.314314e-05
## 5 0.02061553 1.314314e-05
## 6 0.02236068 2.155695e-05
## 7 0.02500000 3.644514e-05
## 8 0.02692582 5.052171e-05
## 9 0.03162278 1.037488e-04
## 10 0.03162278 1.037488e-04
## 11 0.03162278 1.037488e-04
## 12 0.03500000 1.668217e-04
## 13 0.03535534 1.740393e-04
## 14 0.03640055 2.033976e-04
## 15 0.03807887 2.659872e-04
## 16 0.04000000 3.395154e-04
## 17 0.04031129 3.514396e-04
## 18 0.04123106 3.871096e-04
## 19 0.04609772 6.066846e-04
## 20 0.06020797 1.277365e-03
## 21 0.06020797 1.277365e-03
## 22 0.06324555 1.429808e-03
## 23 0.06576473 1.561991e-03
## 24 0.07071068 1.823044e-03
## 25 0.07566373 2.085209e-03
## 26 0.07648529 2.128745e-03
## 27 0.08062258 2.361239e-03
## 28 0.08631338 2.707051e-03
## 29 0.09055385 2.968957e-03
## 30 0.09552487 3.280369e-03
## 31 0.10111874 3.643299e-03
## 32 0.10198039 3.699271e-03
## 33 0.10511898 3.903848e-03
## 34 0.10606602 3.965973e-03
## 35 0.11011358 4.233931e-03
## 36 0.11543396 4.590854e-03
## 37 0.12093387 4.962038e-03
## 38 0.12539936 5.264164e-03
## 39 0.12589678 5.299031e-03
## 40 0.12816006 5.495014e-03
## 41 0.13509256 6.101157e-03
## 42 0.15033296 7.468796e-03
## 43 0.17334936 9.615079e-03
## 44 0.17507141 9.772458e-03
## 45 0.18027756 1.024905e-02
## 46 0.18560711 1.073787e-02
## 47 0.19448650 1.153328e-02
## 48 0.20886599 1.282971e-02
## 49 0.21708293 1.357409e-02
## 50 0.23584953 1.584196e-02
## 51 0.25223997 1.830616e-02
## 52 0.26076810 1.960384e-02
## 53 0.31184932 2.814847e-02
## 54 0.33000000 3.131618e-02
## 55 0.34234486 3.353213e-02
## 56 0.45024993 5.687826e-02
## 57 0.45400991 5.742888e-02
## 58 0.46010868 5.815526e-02
## 59 0.46270941 5.840038e-02
## 60 0.47055818 5.909672e-02
## 61 0.50982840 6.188021e-02
## 62 0.53956001 6.378926e-02
## 63 0.54664888 6.425394e-02
## 64 0.56678920 6.557663e-02
## 65 0.57212324 6.592864e-02
## 66 0.59076222 6.711520e-02
## 67 0.61459336 6.802183e-02
## 68 0.63780875 6.872078e-02
## 69 0.76134749 6.557694e-02
## 70 0.82602966 6.291567e-02
## 71 1.21652168 4.629927e-04
## 72 1.24788822 -4.653744e-03
p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)#Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada) data.c1 <- cbind(data.c[,-4],Y.c)
ggplot(data.c1, aes(x = SHUCKED_WEIGHT, y = Y.c))+geom_point()+labs(title = "SHUCKED_WEIGHT vs. Y") Lo que se está haciendo en realidad es tomar los centros de las observaciones de cada variable predictora como representantes de cada rectángulo de la agrupación rectangular formada por la variable predictora y la variable dependiente del modelo de regresión.
Gráficamente:
shucked_weight1 <- data.frame(lengthmin=c(0.03,0.06,0.07,0.11,0.12,0.16,0.16,0.32,0.00,0.00,0.03,0.06,0.07,0.16,0.11,0.01,0.01,0.02,0.04,0.10,0.11,0.22,0.25,0.38),lengthmax=c(0.64,1.16,1.49,1.23,0.84,0.93,0.82,0.71,0.03,0.50,0.60,0.72,0.77,0.63,0.39,0.02,0.32,1.25,1.35,1.35,1.15,0.87,0.74,0.75)) #variable SHUCKED_WEIGHT
clusters1.3 <- cbind(shucked_weight1,ypred1$Fitted)
colnames(clusters1.3) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos1.3 <- ggplot() + geom_rect(data = clusters1.3,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.2, color = "black"
) +
labs(
title = "Centers for the variable HEIGHT",
x = "HEIGHT",
y = "Y"
) +
theme_minimal()
graf1.3 <- rectangulos1.3 +
geom_point(
data = clusters1.3,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 2, alpha = 0.9
)
graf1.3data.cmasr1 <- cbind(data.cmasr[,-4],Y.cmasr)
ggplot(data.cmasr1, aes(x = SHUCKED_WEIGHT, y = Y.cmasr))+geom_point()+labs(title = "SHUCKED_WEIGHT vs. Y") clusters2.3 <- cbind(shucked_weight1,ypred2$Fitted)
colnames(clusters2.3) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos2.3 <- ggplot() + geom_rect(data = clusters2.3,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers plus ranges for the variable SHUCKED_WEIGHT ", x="SHUCKED_WEIGHT",
y = "Y"
) +
theme_minimal()
graf2.3 <- rectangulos2.3 +
geom_point(
data = clusters2.3,
aes(x = lengthmax, y = ymax),
color = "red", size = 3, alpha = 0.9
)
graf2.3data.cmenosr1 <- cbind(data.cmenosr[,-4],Y.cmenosr)
ggplot(data.cmenosr1, aes(x = SHUCKED_WEIGHT, y = Y.cmenosr))+geom_point()+labs(title = "SHUCKED_WEIGHT vs. Y") clusters3.3 <- cbind(shucked_weight1,ypred3$Fitted)
colnames(clusters3.3) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos3.3 <- ggplot() + geom_rect(data = clusters3.3,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Centers minus ranges for the variable SHUCKED_WEIGHT ",
x = "SHUCKED_WEIGHT",
y = "Y"
) +
theme_minimal()
graf3.3 <- rectangulos3.3 +
geom_point(data = clusters3.3,
aes(x = lengthmin, y = ymin),
color = "green", size = 3, alpha = 0.9
)
graf3.3geom_indicesc <- indice1$results[[4]]$geom_indices #centros
geom_indicescmasr <- indice2$results[[4]]$geom_indices #centrosmasrangos
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el mínimo valor asociado en geom_corr
ggplot(geom_indicescmasr1, aes(x=alpha,y=geom_corr))+geom_point()geom_indicescmenosr <- indice3$results[[4]]$geom_indices #centrosmenosrangos
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el máximo valor asociado en geom_corr
ggplot(geom_indicescmenosr1, aes(x=alpha,y=geom_corr))+geom_point()# Etiquetas para identificar cada curva
geom_indicesc$label <- "centros"
geom_indicescmasr$label <- "centros más rangos"
geom_indicescmenosr$label <- "centros menos rangos"
# Combinar los datos
data_combined <- rbind(geom_indicesc,geom_indicescmasr, geom_indicescmenosr )
data_combined1 <- rbind(geom_indicescmasr1, geom_indicescmenosr1)
# Crear el gráfico
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "Correlación geométrica para la variable SHUCKED_WEIGHT",
x = "Alpha",
y = "Geom_corr",
color = "Curvas"
) +
theme_minimal() +
theme(legend.position = "bottom"))library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmasr1$alpha, geom_indicescmenosr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
ggplot(table.cmasr, aes(x=alpha.vals, geom_corr.cmasr))+geom_point()table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
ggplot(table.cmenosr, aes(x=alpha.vals, geom_corr.cmenosr))+geom_point()## alpha.vals diff.geom_corr
## [1,] 0.01118034 -6.056878e-05
## [2,] 0.01118034 1.496036e-04
## [3,] 0.01581139 4.648621e-04
## [4,] 0.02061553 8.852068e-04
## [5,] 0.02236068 1.095379e-03
## [6,] 0.02500000 2.356413e-03
## [7,] 0.02828427 3.617447e-03
## [8,] 0.03041381 4.247964e-03
## [9,] 0.03201562 6.980205e-03
## [10,] 0.03640055 7.610722e-03
## [11,] 0.03640055 8.031066e-03
## [12,] 0.03640055 8.031066e-03
## [13,] 0.03807887 8.136153e-03
## [14,] 0.04031129 8.661583e-03
## [15,] 0.04031129 9.081928e-03
## [16,] 0.04272002 9.607359e-03
## [17,] 0.04272002 9.607359e-03
## [18,] 0.04924429 1.065822e-02
## [19,] 0.05220153 1.089162e-02
## [20,] 0.05590170 1.071911e-02
## [21,] 0.05852350 1.123065e-02
## [22,] 0.06082763 1.114648e-02
## [23,] 0.06324555 1.130882e-02
## [24,] 0.06519202 1.263236e-02
## [25,] 0.07158911 1.331490e-02
## [26,] 0.07500000 1.323167e-02
## [27,] 0.07905694 1.786537e-02
## [28,] 0.08062258 2.855482e-02
## [29,] 0.08544004 3.174775e-02
## [30,] 0.08732125 3.311988e-02
## [31,] 0.09823441 4.825552e-02
## [32,] 0.09962429 4.866091e-02
## [33,] 0.10124228 6.144676e-02
## [34,] 0.10547512 6.159465e-02
## [35,] 0.10700467 6.074432e-02
## [36,] 0.11101802 5.880626e-02
## [37,] 0.11423660 5.785719e-02
## [38,] 0.11672618 5.934314e-02
## [39,] 0.11800424 5.890536e-02
## [40,] 0.12649111 5.811779e-02
## [41,] 0.13509256 5.768003e-02
## [42,] 0.14534442 5.560988e-02
## [43,] 0.14773287 5.278407e-02
## [44,] 0.15231546 5.067310e-02
## [45,] 0.15508062 4.303702e-02
## [46,] 0.16807736 3.837919e-02
## [47,] 0.17528548 3.217680e-02
## [48,] 0.17585505 2.419068e-02
## [49,] 0.17951323 2.276585e-02
## [50,] 0.18027756 2.248352e-02
## [51,] 0.18445867 2.089791e-02
## [52,] 0.19300259 1.707275e-02
## [53,] 0.20081086 1.635015e-02
## [54,] 0.20892582 1.740634e-02
## [55,] 0.21708293 1.600091e-02
## [56,] 0.22051077 2.126034e-02
## [57,] 0.23264780 4.280093e-02
## [58,] 0.23837995 5.320202e-02
## [59,] 0.24382371 6.146205e-02
## [60,] 0.24824383 6.883527e-02
## [61,] 0.30269622 9.753402e-02
## [62,] 0.30700163 9.446121e-02
## [63,] 0.30809901 9.303622e-02
## [64,] 0.33678628 8.478450e-02
## [65,] 0.37202150 7.965219e-02
## [66,] 0.42323162 7.640330e-02
## [67,] 0.54362211 6.764541e-02
## [68,] 0.54555018 6.349012e-02
## [69,] 0.58234440 5.344916e-02
## [70,] 0.61386073 5.271933e-02
## [71,] 0.62325757 5.016495e-02
## [72,] 0.70178344 4.595081e-02
## [73,] 0.79851425 4.113632e-02
## [74,] 1.31088710 6.716886e-03
## [75,] 1.53075145 -4.536528e-03
## [1] 0.000000e+00 2.595208e-22 2.152799e-06 6.405456e-06 8.317058e-06
## [6] 1.453639e-05 2.641707e-05 3.546328e-05 4.664423e-05 8.001670e-05
## [11] 8.001670e-05 8.001670e-05 9.367174e-05 1.130081e-04 1.130081e-04
## [16] 1.361496e-04 1.361496e-04 2.056867e-04 2.378959e-04 2.775584e-04
## [21] 3.070029e-04 3.326858e-04 3.600297e-04 3.846182e-04 4.697947e-04
## [26] 5.149266e-04 5.874053e-04 6.321118e-04 7.850553e-04 8.473607e-04
## [31] 1.373981e-03 1.441614e-03 1.541034e-03 1.801754e-03 1.894666e-03
## [36] 2.130676e-03 2.316894e-03 2.464633e-03 2.539918e-03 3.033156e-03
## [41] 3.529288e-03 4.099393e-03 4.225465e-03 4.457679e-03 4.576683e-03
## [46] 5.075488e-03 5.307422e-03 5.321200e-03 5.404482e-03 5.421667e-03
## [51] 5.509043e-03 5.654911e-03 5.782578e-03 5.923829e-03 6.054351e-03
## [56] 6.127228e-03 6.646704e-03 6.951666e-03 7.286250e-03 7.590511e-03
## [61] 1.290147e-02 1.330817e-02 1.341026e-02 1.584250e-02 1.864906e-02
## [66] 2.256168e-02 3.070555e-02 3.082796e-02 3.279458e-02 3.445610e-02
## [71] 3.492749e-02 3.853582e-02 4.251497e-02 4.595652e-02 4.495910e-02
## alpha area
## 1 0.01118034 0.000000e+00
## 2 0.01118034 2.595208e-22
## 3 0.01581139 2.152799e-06
## 4 0.02061553 6.405456e-06
## 5 0.02236068 8.317058e-06
## 6 0.02500000 1.453639e-05
## 7 0.02828427 2.641707e-05
## 8 0.03041381 3.546328e-05
## 9 0.03201562 4.664423e-05
## 10 0.03640055 8.001670e-05
## 11 0.03640055 8.001670e-05
## 12 0.03640055 8.001670e-05
## 13 0.03807887 9.367174e-05
## 14 0.04031129 1.130081e-04
## 15 0.04031129 1.130081e-04
## 16 0.04272002 1.361496e-04
## 17 0.04272002 1.361496e-04
## 18 0.04924429 2.056867e-04
## 19 0.05220153 2.378959e-04
## 20 0.05590170 2.775584e-04
## 21 0.05852350 3.070029e-04
## 22 0.06082763 3.326858e-04
## 23 0.06324555 3.600297e-04
## 24 0.06519202 3.846182e-04
## 25 0.07158911 4.697947e-04
## 26 0.07500000 5.149266e-04
## 27 0.07905694 5.874053e-04
## 28 0.08062258 6.321118e-04
## 29 0.08544004 7.850553e-04
## 30 0.08732125 8.473607e-04
## 31 0.09823441 1.373981e-03
## 32 0.09962429 1.441614e-03
## 33 0.10124228 1.541034e-03
## 34 0.10547512 1.801754e-03
## 35 0.10700467 1.894666e-03
## 36 0.11101802 2.130676e-03
## 37 0.11423660 2.316894e-03
## 38 0.11672618 2.464633e-03
## 39 0.11800424 2.539918e-03
## 40 0.12649111 3.033156e-03
## 41 0.13509256 3.529288e-03
## 42 0.14534442 4.099393e-03
## 43 0.14773287 4.225465e-03
## 44 0.15231546 4.457679e-03
## 45 0.15508062 4.576683e-03
## 46 0.16807736 5.075488e-03
## 47 0.17528548 5.307422e-03
## 48 0.17585505 5.321200e-03
## 49 0.17951323 5.404482e-03
## 50 0.18027756 5.421667e-03
## 51 0.18445867 5.509043e-03
## 52 0.19300259 5.654911e-03
## 53 0.20081086 5.782578e-03
## 54 0.20892582 5.923829e-03
## 55 0.21708293 6.054351e-03
## 56 0.22051077 6.127228e-03
## 57 0.23264780 6.646704e-03
## 58 0.23837995 6.951666e-03
## 59 0.24382371 7.286250e-03
## 60 0.24824383 7.590511e-03
## 61 0.30269622 1.290147e-02
## 62 0.30700163 1.330817e-02
## 63 0.30809901 1.341026e-02
## 64 0.33678628 1.584250e-02
## 65 0.37202150 1.864906e-02
## 66 0.42323162 2.256168e-02
## 67 0.54362211 3.070555e-02
## 68 0.54555018 3.082796e-02
## 69 0.58234440 3.279458e-02
## 70 0.61386073 3.445610e-02
## 71 0.62325757 3.492749e-02
## 72 0.70178344 3.853582e-02
## 73 0.79851425 4.251497e-02
## 74 1.31088710 4.595652e-02
## 75 1.53075145 4.495910e-02
p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)#Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada) # Esta curva coincide con la nube de puntos de las diferencias, puesto que es la derivada de la curva obtenida con integración. El máximo alpha obtenido es 0.39HACER LO MISMO CON TODAS LAS OTRAS VARIABLES.
Primero, se tiene una tabla de datos simbólica de tipo intervalo, por ejemplo cardiologicalv2 de RSDA.
Se obtiene la matriz de centros asociada.
Sobre la matriz de centros se aplica un modelo de regresión lineal clásico. Supongamos que se aplica un modelo de regresión lineal tomando como variable de respuesta Pulse.
El modelo es: \(Y=43.9379 + 0.1635X_{1}+0.2109X_{2}-1.4132X_{3}+0.2019X_{4}\).
Luego, se estudia la contribución de cada variable predictora al modelo a través del diagrama de dispersión asociado.
Para la variable Syst, se tiene la nube de puntos:
## Syst Diast Art1 Art2
## Min. : 72.5 Min. : 60.00 Min. :2.500 Min. : 3.500
## 1st Qu.: 89.5 1st Qu.: 83.00 1st Qu.:5.000 1st Qu.: 4.500
## Median :107.0 Median : 86.25 Median :5.750 Median : 5.000
## Mean :111.4 Mean : 88.57 Mean :5.864 Mean : 8.977
## 3rd Qu.:129.0 3rd Qu.: 95.00 3rd Qu.:6.500 3rd Qu.: 8.000
## Max. :160.0 Max. :145.00 Max. :9.500 Max. :45.000
## Y.c
## Min. :62.23
## 1st Qu.:67.44
## Median :73.22
## Mean :74.36
## 3rd Qu.:80.91
## Max. :89.70
Lo que se está haciendo en realidad es tomar los centros de las observaciones de cada variable predictora como representantes de cada rectángulo de la agrupación rectangular formada por la variable predictora y la variable dependiente del modelo de regresión.
Gráficamente:
modelo1 <- sym.lm(Pulse ~ ., sym.data = cardiologicalv2 , method = "cm")
ypred1 <- sym.predict(modelo1, cardiologicalv2)
#length <- cardiologicalv2[c('Syst')]
length1 <- data.frame(lengthmin=c(90,90,140,110,90,130,60,130,110,138,67,56,78,56,56,90,89,89,78,78,78,90,90,90,140,110,90,130,60,130,110,138,67,56,78,56,56,90,89,89,78,78,78,90),lengthmax=c(100,130,180,142,100,160,100,160,190,180, 89,100,130,89,142,89,160,90,160,89,180,150,100,130,180,142,100,160,100,160,190,180,89,100,130,89,142,89,160,90,160,89,180,150))
clusters1 <- cbind(length1,ypred1$Fitted)
colnames(clusters1) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos1 <- ggplot() + geom_rect(data = clusters1,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Agrupación rectangular",
x = "Syst",
y = "Y"
) +
theme_minimal()
graf1 <- rectangulos1 +
geom_point(
data = clusters1,
aes(x = (lengthmin+lengthmax)/2, y = (ymin+ymax)/2),
color = "orange", size = 3, alpha = 0.9
)
graf1 Luego, se calcula el índice de bondad de ajuste geométrico.
## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Estimating R2 Geom for variable = 2
## Estimating R2 Geom for variable = 3
## Estimating R2 Geom for variable = 4
Ahora, además de la matriz de centros se crea la matriz de rangos y se estudian los centros más rangos y los centros menos rangos.
Se crea un modelo de regresión lineal clásico con los centros más rangos.
El modelo es \(Y=68.3611 + 0.1158X_{1}+0.1557X_{2}-1.9050X_{3}+0.2077X_{4}\)
Luego, se estudia la contribución de cada variable predictora al modelo a través del diagrama de dispersión asociado.
data.cmasr1 <- cbind(data.cmasr[,-1],Y.cmasr)
ggplot(data.cmasr1, aes(x = Syst, y = Y.cmasr))+geom_point()+labs(title = "Syst vs. Y") #Nube de puntos LENGTH vs Y.cmasrmodelo2 <- sym.lm(Pulse ~ ., sym.data = cardiologicalv2, method = "crm")
ypred2 <- sym.predict(modelo2, cardiologicalv2)
clusters2 <- cbind(length1,ypred2$Fitted)
colnames(clusters2) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos2 <- ggplot() + geom_rect(data = clusters2,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Agrupación rectangular",
x = "Syst",
y = "Y"
) +
theme_minimal()
graf2 <- rectangulos2 +
geom_point(
data = clusters2,
aes(x = lengthmax, y = ymax),
color = "red", size = 3, alpha = 0.9
)
graf2## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Estimating R2 Geom for variable = 2
## Estimating R2 Geom for variable = 3
## Estimating R2 Geom for variable = 4
Se repite lo anterior, pero ahora usando centros menos rangos.
El modelo es \(Y=32.6549+0.1821X_{1}+0.2440X_{2}-2.0934X_{3}+2913X_{4}\)
data.cmenosr1 <- cbind(data.cmenosr[,-1],Y.cmenosr)
ggplot(data.cmenosr1, aes(x = Syst, y = Y.cmenosr))+geom_point()+labs(title = " Syst vs. Y") modelo3 <- sym.lm(Pulse ~ ., sym.data = cardiologicalv2, method = "crm")
ypred3 <- sym.predict(modelo3, cardiologicalv2)
clusters3 <- cbind(length1,ypred3$Fitted)
colnames(clusters3) <- c('lengthmin','lengthmax','ymin','ymax')
rectangulos3 <- ggplot() + geom_rect(data = clusters3,
aes(xmin = lengthmin, xmax = lengthmax, ymin = ymin, ymax = ymax),
fill = "blue", alpha = 0.1, color = "black"
) +
labs(
title = "Agrupación rectangular",
x = "Syst",
y = "Y"
) +
theme_minimal()
graf3 <- rectangulos3 +
geom_point(data = clusters3,
aes(x = lengthmin, y = ymin),
color = "green", size = 3, alpha = 0.9
)
graf3## Running with x and y
## Index estimation
## Estimating R2 Geom for variable = 1
## Estimating R2 Geom for variable = 2
## Estimating R2 Geom for variable = 3
## Estimating R2 Geom for variable = 4
geom_indicesc <- indice1$results[[1]]$geom_indices #centros
geom_indicescmasr <- indice2$results[[1]]$geom_indices #centrosmasrangos
geom_indicescmasr1 <- geom_indicescmasr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el mínimo valor asociado en geom_corr
ggplot(geom_indicescmasr1, aes(x=alpha,y=geom_corr))+geom_point()geom_indicescmenosr <- indice3$results[[1]]$geom_indices #centrosmenosrangos
geom_indicescmenosr1 <- geom_indicescmenosr %>% group_by(alpha) %>% filter(geom_corr==max(geom_corr)) %>% ungroup() #Selección de los valores únicos de alpha, considerando el máximo valor asociado en geom_corr
ggplot(geom_indicescmenosr1, aes(x=alpha,y=geom_corr))+geom_point()geom_indicesc$label <- "centers"
geom_indicescmasr$label <- "centers plus ranges"
geom_indicescmenosr$label <- "centers minus ranges"
data_combined <- rbind(geom_indicesc,geom_indicescmasr, geom_indicescmenosr )
data_combined1 <- rbind(geom_indicescmasr1, geom_indicescmenosr1)
# Crear el gráfico
ggplotly(ggplot(data_combined, aes(x = alpha, y = geom_corr, color = label)) +
geom_step(size = 1) +
labs(
title = "",
x = "Alpha",
y = "Geom_corr",
color = "Curve"
) +
theme_minimal() +
theme(legend.position = "bottom"))Nota. En los casos en que alpha no cambia, para la curva centros menos rangos se debe utilizar el máximo valor de y, mientras que para la curva centros más rangos, se utilizará centros menos rangos. Todo esto para calcular la integral.
library(pracma)
alpha.vals <- sort(unique(c(geom_indicescmasr1$alpha, geom_indicescmenosr1$alpha)))
geom_corr.cmasr <- approx(geom_indicescmasr1$alpha, geom_indicescmasr1$geom_corr, xout = alpha.vals, rule = 2)$y
geom_corr.cmenosr <- approx(geom_indicescmenosr1$alpha, geom_indicescmenosr1$geom_corr, xout = alpha.vals, rule = 2)$y
diff.geom_corr <- geom_corr.cmasr - geom_corr.cmenosr
table.cmasr <- cbind(alpha.vals, geom_corr.cmasr)
#ggplot(table.cmasr, aes(x=alpha.vals, geom_corr.cmasr))+geom_point()
table.cmenosr <- cbind(alpha.vals, geom_corr.cmenosr)
#ggplot(table.cmenosr, aes(x=alpha.vals, geom_corr.cmenosr))+geom_point()
table.diff <- cbind(alpha.vals, diff.geom_corr)
#ggplot(table.diff, aes(x=alpha.vals, diff.geom_corr))+geom_point()
area.acumulada <- cumsum(c(0, diff.geom_corr[-1] * diff(alpha.vals)))
area.acumulada## [1] 0.000000e+00 4.848795e-05 2.657340e-04 1.800041e-03 1.518320e-02
## [6] 2.804019e-02 2.876162e-02 2.930714e-02 2.958858e-02 2.996462e-02
## [11] 3.163963e-02 3.411002e-02 3.595149e-02 4.025150e-02 4.376838e-02
## [16] 5.260108e-02 6.047286e-02 6.895302e-02 8.807972e-02 1.227884e-01
## [21] 1.227884e-01 1.238813e-01 1.508705e-01 1.691103e-01 1.942478e-01
## [26] 2.038283e-01 2.453912e-01 2.709188e-01 2.709188e-01 3.262522e-01
## [31] 4.504013e-01 4.528516e-01 4.578359e-01 4.630234e-01 4.712916e-01
## [36] 4.822705e-01 4.822705e-01 4.855728e-01 4.934812e-01 5.120535e-01
## [41] 5.143865e-01 5.216714e-01 5.338691e-01 5.338691e-01 6.204609e-01
## [46] 7.104424e-01 8.042832e-01 9.567134e-01 1.444200e+00 1.450849e+00
## [51] 1.455554e+00 1.493681e+00 1.514319e+00 1.514319e+00 1.571764e+00
## [56] 1.608208e+00 1.797918e+00 2.485058e+00 3.201757e+00 3.270675e+00
## [61] 3.385113e+00 3.778692e+00 4.232924e+00 4.624609e+00
## alpha area
## 1 1.402994 0.000000e+00
## 2 1.800061 4.848795e-05
## 3 2.278057 2.657340e-04
## 4 3.214698 1.800041e-03
## 5 4.525922 1.518320e-02
## 6 5.523881 2.804019e-02
## 7 5.565270 2.876162e-02
## 8 5.601771 2.930714e-02
## 9 5.619691 2.958858e-02
## 10 5.660178 2.996462e-02
## 11 5.748418 3.163963e-02
## 12 5.824925 3.411002e-02
## 13 5.872613 3.595149e-02
## 14 5.955429 4.025150e-02
## 15 6.010835 4.376838e-02
## 16 6.122968 5.260108e-02
## 17 6.220597 6.047286e-02
## 18 6.322232 6.895302e-02
## 19 6.538381 8.807972e-02
## 20 6.904634 1.227884e-01
## 21 6.904634 1.227884e-01
## 22 6.916158 1.238813e-01
## 23 7.250422 1.508705e-01
## 24 7.498996 1.691103e-01
## 25 7.791582 1.942478e-01
## 26 7.902273 2.038283e-01
## 27 8.328997 2.453912e-01
## 28 8.577123 2.709188e-01
## 29 8.577123 2.709188e-01
## 30 9.039883 3.262522e-01
## 31 10.042179 4.504013e-01
## 32 10.062766 4.528516e-01
## 33 10.107478 4.578359e-01
## 34 10.156082 4.630234e-01
## 35 10.237990 4.712916e-01
## 36 10.363750 4.822705e-01
## 37 10.363750 4.822705e-01
## 38 10.403056 4.855728e-01
## 39 10.467604 4.934812e-01
## 40 10.598278 5.120535e-01
## 41 10.614784 5.143865e-01
## 42 10.670498 5.216714e-01
## 43 10.759023 5.338691e-01
## 44 10.759023 5.338691e-01
## 45 11.325317 6.204609e-01
## 46 11.823928 7.104424e-01
## 47 12.311073 8.042832e-01
## 48 13.039666 9.567134e-01
## 49 15.011901 1.444200e+00
## 50 15.038705 1.450849e+00
## 51 15.061173 1.455554e+00
## 52 15.251618 1.493681e+00
## 53 15.357607 1.514319e+00
## 54 15.357607 1.514319e+00
## 55 15.761095 1.571764e+00
## 56 16.007865 1.608208e+00
## 57 17.024864 1.797918e+00
## 58 21.191968 2.485058e+00
## 59 25.450041 3.201757e+00
## 60 25.889604 3.270675e+00
## 61 26.442008 3.385113e+00
## 62 30.509817 3.778692e+00
## 63 35.455139 4.232924e+00
## 64 40.465624 4.624609e+00
p <- ggplot(data.acumulada, aes(x = alpha, y = area.acumulada)) +
geom_line(size = 1, color = "blue") +
labs(
title = "Área Acumulada entre las Curvas",
x = "Alpha",
y = "Área Acumulada"
) +
theme_minimal()
ggplotly(p)#Derivada.
tasa.cambio <- diff(area.acumulada) / diff(alpha.vals)
alpha.medios <- (alpha.vals[-1] + alpha.vals[-length(alpha.vals)])/2
data.derivada <- data.frame(alpha = alpha.medios, tasadecambio = tasa.cambio)
p.derivada <- ggplot(data.derivada, aes(x = alpha, y = tasa.cambio)) +
geom_line(size = 1, color = "red") +
labs(
title = "Tasa de Cambio de la Función Acumulada",
x = "Alpha",
y = "Derivada (Tasa de Cambio)"
) +
theme_minimal()
ggplotly(p.derivada)Probar modelos teóricos, datos de tipo intervalo que sigan cierto tipo de distribución o modelos Doughnout por ejemplo.
Idea: análisis de datos complejos
Idea: bondad de ajuste geométrica para datos de tipo histograma
En 0.7 se intersecan las curvas de pérdida
Buscar un mejor representante en vez del centro, no siempre el centro es el mejor representante.
Workshop PaCMAP.
Combinar PaCMAP con el índice propuesto, separar clusters y buscar el mejor representante por cluster.
El objetivo final es devolver una correlación geométrica en intervalo.
Calcular áreas entre curvas entre mayor es el área entre las curvas entonces más agrupados están los rectángulos (gráficamente uno se puede hacer una idea de la contribución por variable con este valor y con la gráfica de las funciones de pérdida).
Sería importante calcular el valor del área bajo la curva para cada alpha. Hay un alpha ideal que aparece en la función spatgeom.
# Optimización por varianza.
opti.varianza <- function (sym.data, num.dimension)
{
N <- sym.data$N
M <- sym.data$M
num.dimen.aux <- num.dimension
seq.min <- seq(from = 1, by = 2, length.out = M)
seq.max <- seq(from = 2, by = 2, length.out = M)
sym.var.names <- sym.data$sym.var.names
sym.data.vertex <- vertex.interval.new.j(sym.data)
sym.data.vertex.matrix <- sym.data.vertex$vertex
dim.vertex <- dim(sym.data.vertex.matrix)[1]
tot.individuals <- N + dim.vertex
min.interval <- as.vector(as.matrix(sym.data$data[, seq.min]))
max.interval <- as.vector(as.matrix(sym.data$data[, seq.max]))
res.min <- nloptr::lbfgs(min.interval, pca.supplementary.vertex.lambda.fun.j,
lower = min.interval, upper = max.interval, nl.info = FALSE,
control = list(xtol_rel = 1e-08, maxeval = 20000), N = N,
M = M, sym.var.names = sym.var.names, sym.data.vertex.matrix = sym.data.vertex.matrix,
tot.individuals = tot.individuals, num.dimen.aux = num.dimen.aux)
M.x <- matrix(res.min$par, nrow = N)
colnames(M.x) <- sym.var.names
M.x <- scale(M.x)
mean.var <- attr(M.x, "scaled:center")
desv.var <- attr(M.x, "scaled:scale")
sym.data.vertex.matrix.cent <- sym.data.vertex.matrix
for (i in 1:M) {
sym.data.vertex.matrix.cent[, i] <- (sym.data.vertex.matrix.cent[,
i] - mean.var[i])/desv.var[i]
}
M.x <- rbind(M.x, sym.data.vertex.matrix.cent)
pca.max <- PCA(X = M.x, scale.unit = FALSE, ind.sup = (N +
1):tot.individuals, ncp = M, graph = FALSE)
pca.min.sym <- sym.interval.pca.limits.new.j(sym.data, pca.max$ind.sup$coord,
sym.data.vertex$num.vertex)
return(list(Sym.Components = pca.min.sym, pca.min = pca.max,
res.max = res.min))
}# Optimización por distancia.
opti.distance <- function (sym.data)
{
N <- sym.data$N
M <- sym.data$M
seq.min <- seq(from = 1, by = 2, length.out = M)
seq.max <- seq(from = 2, by = 2, length.out = M)
sym.var.names <- sym.data$sym.var.names
sym.data.vertex <- vertex.interval.new.j(sym.data)
sym.data.vertex.matrix <- sym.data.vertex$vertex
dim.vertex <- dim(sym.data.vertex.matrix)[1]
tot.individuals <- N + dim.vertex
min.interval <- as.vector(as.matrix(sym.data$data[, seq.min]))
max.interval <- as.vector(as.matrix(sym.data$data[, seq.max]))
init.point <- as.vector(as.matrix(centers.interval.j(sym.data)$centers))
res.min <- nloptr::lbfgs(init.point, pca.supplementary.vertex.fun.j,
lower = min.interval, upper = max.interval, nl.info = FALSE,
control = list(xtol_rel = 1e-08, maxeval = 20000), N = N,
M = M, sym.var.names = sym.var.names, sym.data.vertex.matrix = sym.data.vertex.matrix,
tot.individuals = tot.individuals)
M.x <- matrix(res.min$par, nrow = N)
colnames(M.x) <- sym.var.names
M.x <- scale(M.x)
mean.var <- attr(M.x, "scaled:center")
desv.var <- attr(M.x, "scaled:scale")
sym.data.vertex.matrix.cent <- sym.data.vertex.matrix
for (i in 1:M) {
sym.data.vertex.matrix.cent[, i] <- (sym.data.vertex.matrix.cent[,
i] - mean.var[i])/desv.var[i]
}
M.x <- rbind(M.x, sym.data.vertex.matrix.cent)
pca.min <- FactoMineR::PCA(X = M.x, scale.unit = FALSE,
ind.sup = (N + 1):tot.individuals, ncp = M, graph = FALSE)
pca.min.sym <- sym.interval.pca.limits.new.j(sym.data, pca.min$ind.sup$coord,
sym.data.vertex$num.vertex)
return(list(Sym.Components = pca.min.sym, pca.min = pca.min,
res.min = res.min))
}Primero, se tiene una tabla de datos simbólica de tipo intervalo, por ejemplo abalone de RSDA. Se obtiene la matriz de vértices asociada.
library(RSDA)
datos <- abalone
#Número de vértices de la tabla abalone:
nv <- (2^{dim(datos)[2]})*dim(datos)[1] #3072
#RSDA:::sym.umap.symbolic_tbl()
#RSDA:::expand_rows
vertex <- function(df){
l <- lapply(seq_len(ncol(df)), function(x) list(1, 2))
df_i <- expand.grid(l)
funs <- list(min, max)
funs <- lapply(df_i, function(i) funs[unlist(i)])
out <- lapply(seq_len(nrow(df)), function(i) {
fila <- df[i, ]
out <- lapply(seq_along(funs), function(i) {
unlist(lapply(funs[[i]], function(.f) .f(fila[[i]])))
})
out <- as.data.frame(do.call(cbind.data.frame, out))
colnames(out) <- colnames(df)
return(out)
})
out <- as.data.frame(do.call(rbind.data.frame, out))
colnames(out) <- colnames(df)
return(out)
} #Esta es la funcióne expand_rows del código base de sym.umap
datos.v <- vertex(datos)
datos.v <- round(datos.v, 2)
#Qué pasa si aplico un modelo de regresión para los vérticesmodelo.vertices <- lm(WHOLE_WEIGHT ~., datos.v)
Y.v <- modelo.vertices$fitted.values
Y.v <- round(Y.c,2)Para la variable LENGTH, se tiene la nube de puntos: